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

Guohuan Qiu and Chao Xia

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Submission date: 19. May. 2014 (revised version: May 2014)
Pages: 11
published in: International mathematics research notices, 2015 (2015) 17, p. 7608-7619 
DOI number (of the published article): 10.1093/imrn/rnu184
Bibtex
Keywords and phrases: Reilly's formula, Heintze-Karcher inequality
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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.