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We have decided to discontinue the publication of preprints on our preprint server as of 1 March 2024. The publication culture within mathematics has changed so much due to the rise of repositories such as ArXiV (www.arxiv.org) that we are encouraging all institute members to make their preprints available there. An institute's repository in its previous form is, therefore, unnecessary. The preprints published to date will remain available here, but we will not add any new preprints here.

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