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A generalization of Reilly's formula and its applications to a new Heintze-Karcher type inequality
Guohuan Qiu and Chao Xia
In this paper, we prove a generalization of Reilly's formula in . 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.