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Xuwen Zhang

Publications and source records attributed to Xuwen Zhang.

At least 19 recordsLinked to original sources
arXiv2026

Bernstein theorem for $3$-dimensional anisotropic minimal graphs with free boundary

In this paper, we continue our recent study on anisotropic minimal surface equation with free boundary condition in Wang-Wei-Xia-Zhang (Arch Ration Mech Anal 250:42, 2026). The first main result solves the corresponding mixed boundary value problem. As an application, we prove the following Bernstein-type theorem: any anisotropic minimal graph over $\mathbb{R}^3_+$ with free boundary must be flat. These extend the classical results of Simon (Indiana Univ Math J 25:821--855, 1976; Math Z 154:265--273, 1977) to an appropriate free boundary setting.

math.DG↗
arXiv2026

Regularity of branched stable minimal immersed hypersurfaces

We establish a sharp bound on the Hausdorff dimension of the non-branch singular set of branched stable minimal immersed hypersurfaces whose singular sets have locally finite $\mathcal H^{n-2}$-measure: the non-branch singular set is empty when $n=2$, discrete when $n=3$, and has Hausdorff dimension at most $n-3$ when $n\geq4$. We also construct a non-flat stable minimal cone in $\mathbb R^4$ arising from a branched minimal immersion whose vertex is a non-branch singularity. Taking products with Euclidean factors yields examples whose non-branch singular sets have Hausdorff dimension exactly $n-3$, showing that our regularity bound is sharp in every dimension $n\geq3$. The main ingredients in our proof are a generalized Schoen inequality and a corresponding branched sheeting theorem near stationary classical cones and unions of hyperplanes.

math.DG↗
arXiv2026

SuperSenseDoctor: A Multimodal and Contactless Agent for Health Tracking

Population aging is increasing the need to monitor older adults safely and independently at home. However, cameras, wearables, and manual checks often introduce privacy, adherence, and attention burdens that hinder sustained health monitoring. This paper presents SuperSenseDoctor, a multimodal contactless agent architecture for long-term home health tracking. The system transforms WiFi, mmWave radar, and surface temperature into a persistent human health state. The system relies on fixed decision rules to conduct continuous daily monitoring and respond to pre-defined hazards. When abnormal signals appear, event-driven reasoning analyzes only standardized evidence to produce traceable care-support measures. In this manner, SuperSenseDoctor integrates sensing, temporal state, reasoning, and action into a unified and auditable loop. The calibrated multimodal pipeline achieves 1.994 bpm mean absolute error (MAE) and 3.142 bpm root mean square deviation (RMSD) for heart rate, 0.197 bpm MAE and 0.263 bpm RMSD for respiratory rate, and 96.5% fall-recognition accuracy. The evaluation also covers 2686 one-second states across 9 chronological intervals and reaches a 96.7% criterion-level Agent checklist pass rate. These results demonstrate the feasibility of a stateful contactless sensing-to-action architecture for long-term home health monitoring.

cs.HC↗
arXiv2026

Regularity of stable capillary minimal hypersurfaces

We develop a regularity and compactness theory for stable capillary minimal hypersurfaces in the half-space $\mathbb{H}^{n+1}$ with contact angle $θ\in (0,π)$ and dimension $n \geq 2$. One key analytic ingredient is a capillary differential Schoen inequality, which allows us to establish a boundary sheeting theorem in the spirit of Bellettini. The other ingredient is a refined classification of stable capillary minimal cones, and we show that for any contact angle $θ\in(0,π)$, the stable capillary minimal hypercone in $\mathbb H^5$ with an isolated singularity must be flat. As a consequence, for any $n\leq4$ and $θ\in(0,π)$, we obtain the Bernstein theorem for embedded complete stable capillary minimal hypersurfaces in $\mathbb H^{n+1}$ with Euclidean area growth.

math.DG↗
arXiv2026

A half-space Liouville theorem for anisotropic minimal graph with free boundary

In this paper we prove the following Liouville-type theorem: any anisotropic minimal graph with free boundary in the half-space must be flat, provided that the graph function has at most one-sided linear growth. This extends the classical results of Bombieri-De Giorgi-Miranda and Simon to an appropriate free boundary setting.

math.DG↗
arXiv2025

Emotional Cognitive Modeling Framework with Desire-Driven Objective Optimization for LLM-empowered Agent in Social Simulation

The advent of large language models (LLMs) has enabled agents to represent virtual humans in societal simulations, facilitating diverse interactions within complex social systems. However, existing LLM-based agents exhibit severe limitations in affective cognition: They fail to simulate the bounded rationality essential for bridging virtual and real-world services; They lack empirically validated integration mechanisms embedding emotions within agent decision architectures. This paper constructs an emotional cognition framework incorporating desire generation and objective management, designed to achieve emotion alignment between LLM-based agents and humans, modeling the complete decision-making process of LLM-based agents, encompassing state evolution, desire generation, objective optimization, decision generation, and action execution. This study implements the proposed framework within our proprietary multi-agent interaction environment. Experimental results demonstrate that agents governed by our framework not only exhibit behaviors congruent with their emotional states but also, in comparative assessments against other agent types, demonstrate superior ecological validity and generate decision outcomes that significantly more closely approximate human behavioral patterns.

cs.AI↗
arXiv2025

A Survey on Agentic Service Ecosystems: Measurement, Analysis, and Optimization

The Agentic Service Ecosystem consists of heterogeneous autonomous agents (e.g., intelligent machines, humans, and human-machine hybrid systems) that interact through resource exchange and service co-creation. These agents, with distinct behaviors and motivations, exhibit autonomous perception, reasoning, and action capabilities, which increase system complexity and make traditional linear analysis methods inadequate. Swarm intelligence, characterized by decentralization, self-organization, emergence, and dynamic adaptability, offers a novel theoretical lens and methodology for understanding and optimizing such ecosystems. However, current research, owing to fragmented perspectives and cross-ecosystem differences, fails to comprehensively capture the complexity of swarm-intelligence emergence in agentic contexts. The lack of a unified methodology further limits the depth and systematic treatment of the research. This paper proposes a framework for analyzing the emergence of swarm intelligence in Agentic Service Ecosystems, with three steps: measurement, analysis, and optimization, to reveal the cyclical mechanisms and quantitative criteria that foster emergence. By reviewing existing technologies, the paper analyzes their strengths and limitations, identifies unresolved challenges, and shows how this framework provides both theoretical support and actionable methods for real-world applications.

cs.MA↗
arXiv2025

Half-space Liouville-type theorems for minimal graphs with capillary boundary

In this paper, we prove two Liouville-type theorems for capillary minimal graph over $\mathbb{R}^n_+$. First, if $u$ has linear growth, then for $n=2,3$ and for any $θ\in(0,π)$, or $n\geq4$ and $θ\in(\fracπ6,\frac{5π}6)$, $u$ must be flat. Second, if $u$ is one-sided bounded on $\mathbb{R}^n_+$, then for any $n$ and $θ\in(0,π)$, $u$ must be flat. The proofs build upon gradient estimates for the mean curvature equation over $\mathbb{R}^n_+$ with capillary boundary condition, which are based on carefully adapting the maximum principle to the capillary setting.

math.DG↗
arXiv2025

Varifolds with capillary boundary

In this paper we introduce and study a new class of varifolds in $\mathbf{R}^{n+1}$ of arbitrary dimensions and co-dimensions, which satisfy a Neumann-type boundary condition characterizing capillarity. The key idea is to introduce a Radon measure on a subspace of the trivial Grassmannian bundle over the supporting hypersurface as a generalized boundary with prescribed angle, which plays a role as a measure-theoretic capillary boundary. We show several structural properties, monotonicity inequality, boundary rectifiability, classification of tangent cones, and integral compactness for such varifolds under reasonable conditions. This Neumann-type boundary condition fits very well in the context of curvature varifold and Brakke flow, which we also discuss.

math.DG↗
arXiv2025

Compactness of capillary hypersurfaces with mean curvature prescribed by ambient functions

We prove a compactness result for capillary hypersurfaces with mean curvature prescribed by ambient functions, which generalizes the results of Schätzle and Bellettini to the capillary case. The proof relies on extending the definition of (unoriented) curvature varifolds with capillary boundary introduced by Wang-Zhang to the context of oriented integral varifolds. We also discuss the case when the mean curvature of the boundary is prescribed.

math.DG↗
arXiv2025

Quantitative Alexandrov theorem for capillary hypersurfaces in the half-space

In this paper, we prove the quantitative version of the Alexandrov theorem for capillary hypersurfaces in the half-space, which generalizes Julin-Niinikoski's result to the capillary case. The proof is based on the quantitative analysis of the Montiel-Ros-type argument carried out in our joint works with Wang-Xia.

math.DG↗
arXiv2025

Willmore-type inequality in unbounded convex sets

In this paper we prove the following Willmore-type inequality: On an unbounded closed convex set $K\subset\mathbb{R}^{n+1}$ $(n\ge 2)$, for any embedded hypersurface $Σ\subset K$ with boundary $\partialΣ\subset \partial K$ satisfying a certain contact angle condition, there holds $$\frac1{n+1}\int_Σ\vert{H}\vert^n{\rm d}A\ge{\rm AVR}(K)\vert\mathbb{B}^{n+1}\vert.$$ Moreover, equality holds if and only if $Σ$ is a part of a sphere and $K\setminusΩ$ is a part of the solid cone determined by $Σ$. Here $Ω$ is the bounded domain enclosed by $Σ$ and $\partial K$, $H$ is the normalized mean curvature of $Σ$, and ${\rm AVR}(K)$ is the asymptotic volume ratio of $K$. We also prove an anisotropic version of this Willmore-type inequality. As a special case, we obtain a Willmore-type inequality for anisotropic capillary hypersurfaces in a half-space.

math.DG↗
arXiv2024

Monotonicity Formulas for Capillary Surfaces

In this paper, we establish monotonicity formulas for capillary surfaces in the half-space $\mathbb{R}^3_+$ and in the unit ball $\mathbb{B}^3$ and extend the result of Volkmann (Comm. Anal. Geom.24(2016), no.1, 195~221. \href{https://doi.org/10.4310/CAG.2016.v24.n1.a7}{https://doi.org/10.4310/CAG.2016.v24.n1.a7}) for surfaces with free boundary. As applications, we obtain Li-Yau-type inequalities for the Willmore energy of capillary surfaces, and extend Fraser-Schoen's optimal area estimate for minimal free boundary surfaces in $\mathbb{B}^3$ (Adv. Math.226(2011), no.5, 4011~4030. \href{https://doi.org/10.1016/j.aim.2010.11.007}{https://doi.org/10.1016/j.aim.2010.11.007}) to the capillary setting, which is different to another optimal area estimate proved by Brendle (Ann. Fac. Sci. Toulouse Math. (6)32(2023), no.1, 179~201. \href{https://doi.org/10.5802/afst.1734}{https://doi.org/10.5802/afst.1734}).

math.DG↗
arXiv2024

Computational Experiments Meet Large Language Model Based Agents: A Survey and Perspective

Computational experiments have emerged as a valuable method for studying complex systems, involving the algorithmization of counterfactuals. However, accurately representing real social systems in Agent-based Modeling (ABM) is challenging due to the diverse and intricate characteristics of humans, including bounded rationality and heterogeneity. To address this limitation, the integration of Large Language Models (LLMs) has been proposed, enabling agents to possess anthropomorphic abilities such as complex reasoning and autonomous learning. These agents, known as LLM-based Agent, offer the potential to enhance the anthropomorphism lacking in ABM. Nonetheless, the absence of explicit explainability in LLMs significantly hinders their application in the social sciences. Conversely, computational experiments excel in providing causal analysis of individual behaviors and complex phenomena. Thus, combining computational experiments with LLM-based Agent holds substantial research potential. This paper aims to present a comprehensive exploration of this fusion. Primarily, it outlines the historical development of agent structures and their evolution into artificial societies, emphasizing their importance in computational experiments. Then it elucidates the advantages that computational experiments and LLM-based Agents offer each other, considering the perspectives of LLM-based Agent for computational experiments and vice versa. Finally, this paper addresses the challenges and future trends in this research domain, offering guidance for subsequent related studies.

cs.AI↗
arXiv2023

Heintze-Karcher inequality and capillary hypersurfaces in a wedge

In this paper, we utilize the method of Heintze-Karcher to prove a "best" version of Heintze-Karcher-type inequality for capillary hypersurfaces in the half-space or in a wedge. One of new crucial ingredients in the proof is modified parallel hypersurfaces which are very natural to be used to study capillary hypersurfaces. A more technical part is a subtle analysis along the edge of a wedge. As an application, we classify completely embedded capillary constant mean curvature hypersurfaces that hit the edge in a wedge, which is a subtler case.

math.DG↗
arXiv2023

Rigidity and quantitative stability for partially overdetermined problems and capillary CMC hypersurfaces

In this paper, we first prove a rigidity result for a Serrin-type partially overdetermined problem in the half-space, which gives a characterization of capillary spherical caps by the overdetermined problem. In the second part, we prove quantitative stability results for the Serrin-type partially overdetermined problem, as well as capillary almost constant mean curvature hypersurfaces in the half-space.

math.AP↗