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MiS Preprint
54/2014

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

Guohuan Qiu and Chao Xia

Abstract

In this paper, we prove a generalization of Reilly's formula in [10]. 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.

Received:
May 19, 2014
Published:
May 19, 2014
Keywords:
Reilly's formula, Heintze-Karcher inequality

Related publications

inJournal
2015 Repository Open Access
Guohuan Qiu and Chao Xia

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

In: International mathematics research notices, 2015 (2015) 17, pp. 7608-7619