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

By Guohuan Qiu, Chao Xia. 2014

85 citations recorded by the source corpus.

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.

Subfields: Applied Mathematics

View Paper: https://www.semanticscholar.org/paper/02ed64fe13653048e36611a6eacdec78e037b1f3

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In Applied Mathematics

1. Chao Xia
2. Junfang Li
3. Xiaodong Cao
4. Guofang Wang
5. Yong Wei

Citations in the corpus

• An integral formula and its applications on sub-static manifolds (2016, methodology): “This formula generalizes Reilly’s original formula from [15] and the recent result from [17].”