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Xuan Yao

Publications and source records attributed to Xuan Yao.

At least 19 recordsLinked to original sources
arXiv2026

A Poincare-Einstein Liouville Theorem and the Yamabe Invariant of Lens Spaces

Schoen conjectured that the Yamabe invariant of every lens space is achieved by the round metric. A proof of this conjecture is presented for all lens spaces, together with rigidity: equality is only achieved for the round class. The key step is to show that every $\mathbb Z_p$-invariant Yamabe-positive conformal class on $S^3$ admits a $\mathbb Z_p$-equivariant Poincaré-Einstein filling. The distance function from a fixed point of the filling then gives an invariant test function with Yamabe quotient at most $σ(S^3)$, which descends to the lens space. The proof of the main theorem was generated by AI (ChatGPT Astra, September 2026); this is mainly a learning note of the AI generated proof.

math.DG↗
arXiv2026

Capillary minimal slicing and scalar curvature rigidity

We develop minimal slicing via capillary hypersurfaces to understand scalar curvature metric on manifolds bounded below with boundary. In particular, in dimension $4$, we prove following comparison and rigidity statement: given a compact Riemannian $4$-manifold $(M^4,g)$ with a mean convex boundary whose boundary is diffeomorphic to boundary of a connected convex domain in $\mathbb R^4$, if the scalar curvature is non-negative and the scaled mean curvature comparison holds along the boundary, then $M$ is isometric to the Euclidean domain. Moreover, we prove a comparison and rigidity result of manifolds with Listing type scaling invariant scalar and mean curvature comparison : $R g \ge -12 g_{\mathbb{H}^{4}}$ and $\hat{H}^{2} g \ge \hat{H}_{0} g_{\mathbb{H}^{4}}$, where $\hat{H}$ is a shifted mean curvature depending on the scale of manifold. This proves the traced version of Gromov's conjecture on comparison and rigidity of hyperbolic convex domains

math.DG↗
arXiv2026

Regime-Aware Interpretable Ranking for Sector Rotation

Sector rotation is a common decision in benchmark-relative portfolio management, where portfolio managers rank sectors for overweight and underweight positions. We formulate this task as ranking sector actions by expected future risk-adjusted active performance, measured with forward sector-benchmark Sharpe ratios. Such rankings should preserve temporal information, express model outputs through economically familiar signal characteristics, account for changes in signal relevance across macroeconomic environments, and capture dependencies among sectors. We propose RegimeRank, an interpretable sector-ranking model that represents fundamental and technical signals through expert-defined temporal characteristics, conditions them on learned macro factors via cross-attention, and models cross-sector dependencies through self-attention. Expected-gradient attributions identify the contributions of individual signal-transformation pairs, while macroeconomic and cross-sector attention maps provide diagnostics of the learned conditioning and relational structure. We evaluate RegimeRank on weekly S&P 500 data from 2002 to 2024 under combinatorial purged cross-validation, where it outperforms representative ranking and machine-learning baselines across multiple ranking metrics. Ablation studies support the contributions of latent macro states, regime conditioning, and cross-sector modelling, while attribution and attention analyses illustrate the temporal characteristics, macro states, and sector relationships underlying its rankings.

q-fin.PM↗
arXiv2026

FinNextAssist: Towards Professional Financial Deep Research Assistant

Deep Research (DR) agents have demonstrated strong capabilities in complex, research-oriented tasks through autonomous planning, iterative retrieval, multi-step reasoning, and structured reporting. However, adapting DR agents to finance introduces unique challenges: financial analysis demands the joint completion of heterogeneous sub-tasks spanning diverse data types, tools, and analytical workflows. We identify three key requirements for a professional financial DR agent: integration of authoritative, heterogeneous financial data sources; specialized analytical tools and skills; and dedicated sub-agents for domain-specific sub-tasks. Building on these principles, we propose FinNextAssist, an end-to-end deep research framework designed for professional financial analysis. FinNextAssist decomposes the research process into four stages: Task Planner, Evidence Compiler, Reasoning Engine, and Report Assembler, and introduces two novel lightweight sub-agents: TabAgent, for cross-market financial table understanding, and HeteroAgent, for cross-modality heterogeneous financial data interpretation. Extensive experiments on FinDeepResearch, the Finance Agent Benchmark, and FinTMMBench-Web show that FinNextAssist substantially outperforms both strong proprietary and open-source DR agents, with ablation studies confirming the contribution of each component across diverse markets and languages.

cs.MA↗
arXiv2026

Scalar Curvature Lower Bounds and Convergence in Measure

Assume that smooth metrics $g_k$ converge in measure to a smooth metric $g$. Gromov asked the following question: if all the metrics $g_k$ have non-negative scalar curvature does it follow that $g$ also has non-negative scalar curvature? We answer Gromov's question in dimension three. We show that, without further assumptions, the metric $g$ need not have non-negative scalar curvature and in fact $g$ may be completely arbitrary. However, if one assumes in addition that the identity maps $(M,g_k)\to (M,g)$ are uniformly bi-Lipschitz, then indeed $g$ must have non-negative scalar curvature. Our method of proof can also be used to show that, under an almost Euclidean entropy condition, scalar curvature lower bounds will persist under convergence of the metrics together with their inverses in $L^p$ for suitably large $p$.

math.DG↗
arXiv2026

DelistBench: Evaluating Search-Enabled LLMs for Auditable Corporate-Event Database Completion

Financial institutions need an independent way to detect missing, stale, and misclassified corporate-event records in vendor databases. We introduce Search-to-Record, a database-assurance task in which search-enabled large language models reconstruct institution-defined event records from public sources for a known security universe and historical cutoff, and DelistBench, a 1,200-record benchmark for security-level delisting announcements. We evaluate five models in paired closed-book and web-enabled conditions. Web access raises announcement-date accuracy within seven days by 34.0 to 48.0 percentage points and event-status accuracy by approximately 2.8 to 21.7 points; the best system achieves 81.5% overall joint accuracy within seven days. Economy web systems achieve 75.9-78.3% overall joint accuracy within seven days at 4.5-6.6% of the API cost of the most expensive web system. Risk-based triage identifies low-error subsets, although the highest-coverage operating point still sends 27.3% of the balanced test set to review. The evaluation identifies web retrieval as the main source of timing gains and shows that low-cost systems can approach the best system's accuracy. Together, Search-to-Record, DelistBench, and the evaluation provide concrete deployment guidance: calibrate triage to local event prevalence and market mix, preserve positive-event recall, and route positive and ambiguous cases to targeted review.

cs.CL↗
arXiv2026

SC$^{2}$-WM: A Self-Correcting World Model with Closed-Loop Feedback for Vision-and-Language Navigation in Continuous Environments

Vision-and-Language Navigation in Continuous Environments (VLN-CE) requires agents to make fine-grained navigation decisions under partial observability. However, most existing methods rely on open-loop execution, lacking mechanisms to detect and correct internal state drift during inference. We propose SC$^{2}$-WM, a self-correcting world model framework that introduces internal feedback for closed-loop decision making in VLN-CE. Our method derives feedback from world-model foresight to perform state-level plan refinement before action execution. To handle challenging scenarios, we further introduce conditional world-aware adaptation, which enables model-level correction by selectively updating the world model at test time when feedback indicates model capacity insufficiency. Experiments on standard VLN-CE benchmarks demonstrate improved navigation robustness and generalization. Our code is available at https://github.com/sunrise-ikun/SC2_WM.

cs.RO↗
arXiv2026

Who Wins Where? Conformal Model Comparison for Local Superiority

Standard model comparison is global, aggregating losses across the covariate space to declare a single winner. This can obscure heterogeneous performance, where different models are preferable in different regions. We introduce conformalized local model comparison, a split-sample framework for constructing calibrated local best-model maps. Given a model comparison score, such as the difference between two squared losses, the method uses three disjoint splits to fit competing models, estimate local centers and scales from out-of-sample scores, and conformally calibrate residual uncertainty. At a target point, the procedure declares a local winner only when a one-sided conformal bound excludes a tie, with the score's sign determining the favored model. We prove finite-sample marginal control for one-sided erroneous declarations on the realized future comparison score, establish pointwise consistency of the localized mean-score estimator away from tie boundaries, show that aggregate comparison can disagree sharply with the prevalence of local superiority, and derive a squared-loss bias--variance decomposition that clarifies how model structure affects local wins. Synthetic and real-data experiments show that the method recovers heterogeneous winner regions, abstains under uncertainty, and yields higher conditional gain than global selection.

cs.LG↗
arXiv2026

A Positive Mass Theorem for Continuous Metrics

Let $g$ be a continuous metric on $\mathbb R^3$ which is asymptotically flat in the sense that $\vert g_{ij}(x) - δ_{ij}\vert = O(\vert x\vert^{-τ})$ for some $τ> \frac{1}{2}$. Further assume that $g$ can be uniformly approximated on compact sets by smooth metrics with almost non-negative scalar curvature. For such a metric $g$, we define a synthetic ADM mass $m(g)$ using harmonic functions. The harmonic mass $m(g)$ coincides with the usual ADM mass whenever $g$ is smooth and decays rapidly enough that the latter is defined. The harmonic mass can also be computed as a limit of the $C^0$ local mass introduced by Burkhardt-Guim. Our main result is a positive mass theorem: the harmonic mass satisfies $m(g)\geq 0$ and if $m(g) = 0$ then $g$ is flat.

math.DG↗
arXiv2026

Scalar curvature under weak limits of manifolds

We show that scalar curvature lower bounds are preserved under certain weak convergence of smooth three manifolds to a smooth limit. More precisely, suppose that $M_k$ and $M$ are smooth, closed, Riemannian three manifolds. Assume that there are smooth, surjective, $λ_k$-Lipschitz maps $f_k\colon M_k \to M$ and that $\text{Vol}(M_k)\to \text{Vol}(M)$ and $λ_k\to 1$. Then if each $M_k$ has scalar curvature bounded below by $κ$ so does $M$. This result answers questions of Gromov, Sormani, Allen, and others. The proof relies on a delicate comparison between $μ$-bubbles in $M_k$ and $μ$-bubbles in $M$.

math.DG↗
arXiv2026

Quantification of $C^0$ Convergence in Dimension Three

We address Gromov's Quantification of $C^0$ Convergence Conjecture in dimension three. Let $B$ be the unit ball in $\mathbb R^3$. Let $g$ and $g_0$ be smooth metrics on $B$. We prove there are constants $C$ and $ε_0$ depending only on $g_0$ so that \[ \inf_{x\in B} R_g(x) \leq R_{g_0}(0) + C \|g-g_0\|_{C^0}^{1/2} \] provided $\|g-g_0\|_{C^0}\leq ε_0$. We also construct examples to show that the exponent $1/2$ is sharp. This explicitly quantifies the fact that scalar curvature lower bounds are preserved under $C^0$ convergence of metrics. When $g_0$ is merely $C^2$ we prove a related estimate with a slightly weaker rate, and when $g_0$ has rotational symmetry we prove a related estimate with a stronger linear rate. To prove these results, we use harmonic functions to define a local quantity that detects the scalar curvature. Then we use classical elliptic PDE estimates to show that this quantity is stable under $C^0$ perturbations of the metric. As a further application of this method, we give a partial answer to a question of Gromov on the preservation of scalar curvature lower bounds for metrics that are converging in measure.

math.DG↗
arXiv2026

FinDeepForecast: A Live Multi-Agent System for Benchmarking Deep Research Agents in Financial Forecasting

Deep Research (DR) Agents powered by advanced Large Language Models (LLMs) have fundamentally shifted the paradigm for completing complex research tasks. Yet, a comprehensive and live evaluation of their forecasting performance on real-world, research-oriented tasks in high-stakes domains (e.g., finance) remains underexplored. We introduce FinDeepForecast, the first live, end-to-end multi-agent system for automatically evaluating DR agents by continuously generating research-oriented financial forecasting tasks. This system is equipped with a dual-track taxonomy, enabling the dynamic generation of recurrent and non-recurrent forecasting tasks at both corporate and macro levels. With this system, we generate FinDeepForecastBench, a weekly evaluation benchmark over a ten-week horizon, encompassing 8 global economies and 1,314 listed companies, and evaluate 13 representative methods. Extensive experiments show that, while DR agents consistently outperform strong baselines, their performance still falls short of genuine forward-looking financial reasoning. We expect the proposed FinDeepForecast system to consistently facilitate future advancements of DR agents in research-oriented financial forecasting tasks. The benchmark and leaderboard are publicly available on the OpenFinArena Platform.

cs.MA↗
arXiv2026

FinDeepResearch: Evaluating Deep Research Agents in Rigorous Financial Analysis

Deep Research (DR) agents, powered by advanced Large Language Models (LLMs), have recently garnered increasing attention for their capability in conducting complex research tasks. However, existing literature lacks a rigorous and systematic evaluation of DR Agent's capabilities in critical research analysis. To address this gap, we first propose HisRubric, a novel evaluation framework with a hierarchical analytical structure and a fine-grained grading rubric for rigorously assessing DR agents' capabilities in corporate financial analysis. This framework mirrors the professional analyst's workflow, progressing from data recognition to metric calculation, and finally to strategic summarization and interpretation. Built on this framework, we construct a FinDeepResearch benchmark that comprises 64 listed companies from 8 financial markets across 4 languages, encompassing a total of 15,808 grading items. We further conduct extensive experiments on the FinDeepResearch using 16 representative methods, including 6 DR agents, 5 LLMs equipped with both deep reasoning and search capabilities, and 5 LLMs with deep reasoning capabilities only. The results reveal the strengths and limitations of these approaches across diverse capabilities, financial markets, and languages, offering valuable insights for future research and development. The benchmark and evaluation code is publicly available at https://OpenFinArena.com/.

cs.CL↗
arXiv2025

Stable Bernstein Problem in certain positively curved manifolds

We formulate stable Bernstein type theorems in certain positively curved ambient manifolds. In all dimensions, we prove that for any complete Riemannian manifold $(X^{n+1},g)$, if the Ricci curvature is non-negative and it positive BiRic curvature with $α$-decay, then any complete, two-sided, stable minimal immersion must be totally geodesic and $\text{Ric}(ν,ν)$ vanish along the minimal immersion. For $4\leq n+1\leq 6$, we prove that the result still holds if $(X^{n+1},g)$ has uniform positive $3$-intermediate curvature and non-negative $(n-1)$-Ricci curvature, which generalize Chodosh-Li-Stryker's result \cite{chodosh2024complete} for $n+1=4$ to higher dimensions. As an immediate corollary, we show that, in all dimensions, for a complete Riemannian manifold $(X^{n+1},g)$, if it has uniform positive Ricci curvature and non-negative $(n-1)$-Ricci curvature then there is no (not necessarily) complete, two-sided, stable minimal immersion in $(X^{n+1},g)$.

math.DG↗
arXiv2025

Evaluating Large Language Models for Financial Reasoning: A CFA-Based Benchmark Study

The rapid advancement of large language models presents significant opportunities for financial applications, yet systematic evaluation in specialized financial contexts remains limited. This study presents the first comprehensive evaluation of state-of-the-art LLMs using 1,560 multiple-choice questions from official mock exams across Levels I-III of CFA, most rigorous professional certifications globally that mirror real-world financial analysis complexity. We compare models distinguished by core design priorities: multi-modal and computationally powerful, reasoning-specialized and highly accurate, and lightweight efficiency-optimized. We assess models under zero-shot prompting and through a novel Retrieval-Augmented Generation pipeline that integrates official CFA curriculum content. The RAG system achieves precise domain-specific knowledge retrieval through hierarchical knowledge organization and structured query generation, significantly enhancing reasoning accuracy in professional financial certification evaluation. Results reveal that reasoning-oriented models consistently outperform others in zero-shot settings, while the RAG pipeline provides substantial improvements particularly for complex scenarios. Comprehensive error analysis identifies knowledge gaps as the primary failure mode, with minimal impact from text readability. These findings provide actionable insights for LLM deployment in finance, offering practitioners evidence-based guidance for model selection and cost-performance optimization.

cs.CL↗
arXiv2025

NavMorph: A Self-Evolving World Model for Vision-and-Language Navigation in Continuous Environments

Vision-and-Language Navigation in Continuous Environments (VLN-CE) requires agents to execute sequential navigation actions in complex environments guided by natural language instructions. Current approaches often struggle with generalizing to novel environments and adapting to ongoing changes during navigation. Inspired by human cognition, we present NavMorph, a self-evolving world model framework that enhances environmental understanding and decision-making in VLN-CE tasks. NavMorph employs compact latent representations to model environmental dynamics, equipping agents with foresight for adaptive planning and policy refinement. By integrating a novel Contextual Evolution Memory, NavMorph leverages scene-contextual information to support effective navigation while maintaining online adaptability. Extensive experiments demonstrate that our method achieves notable performance improvements on popular VLN-CE benchmarks. Code is available at https://github.com/Feliciaxyao/NavMorph.

cs.CV↗
arXiv2025

Scalar curvature comparison and rigidity of $3$-dimensional weakly convex domains

For a compact Riemannian $3$-manifold $(M^{3}, g)$ with mean convex boundary which is diffeomorphic to a weakly convex compact domain in $\mathbb{R}^{3}$, we prove that if scalar curvature is nonnegative and the scaled mean curvature comparison $H^{2}g \ge H_{0}^{2} g_{Eucl}$ holds, then $(M,g)$ is flat. Our result is a smooth analog of Gromov's dihedral rigidity conjecture and an effective version of extremity results on weakly convex balls in $\mathbb R^3$. More generally, we prove the comparison and rigidity theorem for several classes of manifold with corners. Our proof uses capillary minimal surfaces with prescribed contact angle together with the construction of foliation with nonnegative mean curvature and with prescribed contact angles.

math.DG↗