Caiyan Li

activity

20222026

collaborators

5 papers

math.AP2026

Failure of Interior Hölder and Gradient Estimates for the Subcritical Special Lagrangian Equation

Zhenyu Fan, Caiyan Li, Zhehui Wang

For every $n \geq 3$ , we show, by a family of explicit entire real-analytic solutions, that, for every subcritical phase and every $0 < α \leq 1$ , oscillation-based interior $C^{α}$ estimate…

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.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…