Caiyan Li

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20222026

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6 papers · 1 filter

math.DG2026

Alexandrov-Type Rigidity for Minimal Capillary Hypersurfaces on Rotational Supports

Caiyan Li, Chao Xia

In this paper, we prove that, under suitable conditions on the generating profile, every connected, compact embedded minimal capillary hypersurface supported on a one-ended rotatio…

math.DG2026

A Horizon-Free Extrinsic Penrose Inequality

Caiyan Li

Let $S \subset R^{3}$ be a properly embedded mean-convex planar surface with finitely many ends. Designate one end as asymptotically flat, assume that $H_{S}$ is integrable there…

math.DG2026

Positive Mass Theorem with Arbitrary Ends and Noncompact Boundary

Caiyan Li

We prove a positive mass theorem for complete Riemannian manifolds with noncompact boundary, a distinguished asymptotically flat half-space end, and finitely many additional comple…

math.DG2026

Blow-up phenomena for the constant Q/R-curvature equation

Caiyan Li, Guofang Wang, Wei Wei

Let $n \geq 25$ be an integer. In this paper, we construct a Riemannian metric $g_{0}$ on $S^{n}$ , smooth for $n \geq 26$ and of class $C^{9}$ but not $C^{10}$ for $n = 25$ , with t…

math.DG2025

The Dirichlet problem for the minimal surface system on smooth domains

Caiyan Li, Hengyu Zhou

In this paper, we propose a new assumption (1.2) that involves a small oscillation and $C^{2}$ norms for maps from smooth bounded domains into Euclidean spaces. Furthermore, by assum…

math.DG2022

Boundary behaviors of spacelike constant mean curvature surfaces in Schwarzschild spacetime

Caiyan Li, Yuguang Shi, Luen-Fai Tam

We prove that a spacelike spherical symmetric constant mean curvature (SSCMC) surface and a general spacelike constant mean curvature (CMC) surface with certain boundary condition…