A generalization of Reilly's formula and its applications to a new Heintze-Karcher type inequality

Guohuan Qiu; Chao Xia

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arXiv · 1405.4518

A generalization of Reilly's formula and its applications to a new Heintze-Karcher type inequality

Guohuan Qiu·Chao Xia

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Abstract

In this paper, we prove a generalization of Reilly's formula in \cite{Reilly}. We apply such general Reilly's formula to give alternative proofs of the Alexandrov's Theorem and the Heintze-Karcher inequality in the hemisphere and in the hyperbolic space. Moreover, we use the general Reilly's formula to prove a new Heintze-Karcher inequality for Riemannian manifolds with boundary and sectional curvature bounded below.

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Guohuan Qiu, Chao Xia. 2014-05-18. A generalization of Reilly's formula and its applications to a new Heintze-Karcher type inequality. https://arxiv.org/abs/1405.4518

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