发表机构
School of Mathematical Sciences, Xiamen University（厦门大学数学科学学院）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文证明了在超二次体积增长下，具有凸边界、受夹Ricci张量和第二基本形式的完备连通三维流形等距于欧几里得半空间，采用位势论方法。
AI 中文摘要
我们证明了在超二次体积增长假设下，Ricci-受夹三维流形的刚性定理的边界类比。更精确地，我们证明了一个具有凸边界、受夹的Ricci张量和受夹的第二基本形式的完备连通三维流形等距于欧几里得半空间。证明是位势论的。我们构造并研究了混合Dirichlet-Neumann $p$-容度势，建立了其自由边界水平集的单调性公式，并使用适用于此设置的弱Gauss-Bonnet公式。
英文摘要
We prove a boundary analogue of the rigidity theorem for Ricci-pinched three-manifolds under a superquadratic volume-growth assumption. More precisely, we show that a complete connected three-manifold with convex boundary, pinched Ricci tensor, and pinched second fundamental form is isometric to the Euclidean half-space. The proof is potential-theoretic. We construct and study mixed Dirichlet--Neumann $p$-capacitary potentials, establish monotonicity formulas for their free-boundary level sets, and use a weak Gauss--Bonnet formula adapted to this setting.
Comments46 pages
