Author

Caiyan Li

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Preprint Aug 2026

A Horizon-Free Extrinsic Penrose Inequality

Let $S\subset\mathbb R^3$ 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, and denote its extrinsic mass by $m_+(S)$. Let $A_S$ be the infimum of the areas of compact surfaces separating the distinguished end from...

Cai-Yan Li · 1 citation

Preprint Aug 2026

Positive Mass Theorem with Arbitrary Ends and Noncompact Boundary

We prove a positive mass theorem for complete Riemannian manifolds with noncompact boundary, a distinguished asymptotically flat half-space end, and finitely many additional complete ends with no prescribed asymptotics. If $3\leq n\leq7$, $R_g\geq0$, and $H_{\partial M}\geq0$, then $ \mathfrak m(M,g,\mathcal E)\geq0$....

Caiyan Li · 1 citation