Caiyan Li

activity

20222026

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5 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.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.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…