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

摘要

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