arXiv subjects

Mingxuan Yang

Publications and source records attributed to Mingxuan Yang.

7 recordsLinked to original sources

arXiv2026

Rigidity of stable spacelike capillary hypersurfaces in de Sitter and Minkowski spaces

We prove a rigidity theorem for compact spacelike capillary hypersurfaces in de~Sitter and Minkowski spaces: volume-preserving stability forces total umbilicity when the support is a spacelike totally umbilical hypersurface of nonnegative intrinsic curvature. Using the light-cone model, we construct conformal Killing fields tangent to the support and derive a unified Minkowski-type formula valid in all Lorentzian space forms. The resulting mean-zero functions satisfy an inhomogeneous Jacobi equation and the linearized capillary Robin boundary condition, and form canonical finite-dimensional test families. A finite-trace identity, supplemented in the de~Sitter cases by a nonpositive Dirichlet Green correction, detects the umbilicity defect $n|h|^2-H^2$ with a definite sign; hence, every non-totally-umbilical hypersurface admits an admissible test function with positive second variation. The construction extends to supports of negative intrinsic curvature, where a unique timelike parameter direction prevents the finite trace from being sign-definite.

math.DG↗

arXiv2026

SemEval-2026 Task 12: Abductive Event Reasoning: Towards Real-World Event Causal Inference for Large Language Models

Understanding why real-world events occur is important for both natural language processing and practical decision-making, yet direct-cause inference remains underexplored in evidence-rich settings. To address this gap, we organized SemEval-2026 Task 12: Abductive Event Reasoning (AER).\footnote{The task data is available at https://github.com/sooo66/semeval2026-task12-dataset.git} The task asks systems to identify the most plausible direct cause of a target event from supporting evidence. We formulate AER as an evidence-grounded multiple-choice benchmark that captures key challenges of real-world causal reasoning, including distributed evidence, indirect background factors, and semantically related but non-causal distractors. The shared task attracted 122 participants and received 518 submissions. This paper presents the task formulation, dataset construction pipeline, evaluation setup, and system results. AER provides a focused benchmark for abductive reasoning over real-world events and highlights challenges for future work on causal reasoning and multi-document understanding.

cs.CL↗

arXiv2025

Positive determinacy of h-Shuhan matrices with $h<2$

In this paper, we define h-Shuhan matrix, which is the generalization of the generalized Cartan matrix, and find the h-Shuhan matrices for all positive semi-definite ( or generalized positive semi-definite, virtual positive semi-definite) with $h<2$. Furthermore, we know that the largest eigenvalue of the matrix $\hat{B}_{n}^{h}$ increases with $n$, but it is always less than $h$ plus a constant $ε\approx2.04998$.

math.RA↗

arXiv2024

Anisotropic capillary hypersurfaces in a wedge

We investigate anisotropic capillary hypersurfaces within a wedge in Euclidean space. In this study, we generalize the Minkowski norm $F$, traditionally employed to define the anisotropic surface energy, to a gauge on the unit sphere $S^n$. This generalization helps to illuminate a significant relationship between capillary hypersurfaces and hypersurfaces with free boundary. Our main results include new Minkowski formulae and a Heintze-Karcher type inequality. As an application, we prove an Alexandrov-type theorem, thereby extending the known results to the anisotropic setting.

math.DG↗

arXiv2024

Square commutative groups

In this paper we first give a necessary and sufficient condition for a group $G$ generated by $n$ elements to be a square commutative group and prove $G$ is a square commutative group if and only if $\widehat{G}$ is an abelian group, then we give conditions for a group generated by two elements, with additional conditions, to be a square commutative group.

math.GR↗

arXiv2023

Overdetermined problems for fully nonlinear equations with constant Dirichlet boundary conditions in space forms

We consider overdetermined problems for two classes of fully nonlinear equations with constant Dirichlet boundary conditions in a bounded domain in space forms. We prove that if the domain is star-shaped, then the solution to the Hessian quotient overdetermined problem is radially symmetric. By establishing a Rellich-Pohožaev type identity for the $k$-Hessian equation with constant Dirichlet boundary condition, we also show the radial symmetry of the solution to the $k$-Hessian overdetermined problem for some boundary value without star-shapedness assumption of the domain.

math.AP↗

arXiv2023

A partially overdetermined problem for $p$-Laplace equation in convex cones

We consider a partially overdetermined problem for the $p$-Laplace equation in a convex cone $\mathcal{C}$ intersected with the exterior of a smooth bounded domain $\overlineΩ$ in $\mathbb{R}^n$($n\geq2$). First, we establish the existence, regularity, and asymptotic behavior of a capacitary potential. Then, based on these properties of the potential, we use a $P$-function, the isoperimetric inequality, and the Heintze-Karcher type inequality in a convex cone to obtain a rigidity result under the assumption of orthogonal intersection.

math.AP↗