A Generalization of Reilly's Formula and its Applications to a New Heintze–Karcher Type Inequality

Autor:	Chao Xia, Guohuan Qiu
Rok vydání:	2014
Předmět:	Pure mathematics Generalization General Mathematics Hyperbolic space Mathematics::General Topology Boundary (topology) Type inequality Mathematics::Spectral Theory Mathematical proof Algebra Bounded function Mathematics::Differential Geometry Sectional curvature Mathematics
Zdroj:	International Mathematics Research Notices. 2015:7608-7619
ISSN:	1687-0247 1073-7928
DOI:	10.1093/imrn/rnu184
Popis:	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.
Databáze:	OpenAIRE
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