# Weighted Hsiung-Minkowski formulas and rigidity of umbilical hypersurfaces

Kwong Kwok-Kun, Hojoo Lee, Juncheol Pyo

4 引文 斯高帕斯（Scopus）

## 摘要

We use the weighted Hsiung-Minkowski integral formulas and Brendle’s inequality to show new rigidity results. We prove Alexandrov type results for closed embedded hypersurfaces with radially symmetric higher order mean curvature in a large class of Riemannian warped product manifolds, including the Schwarzschild and Reissner-Nordström spaces, where the Alexandrov reflection principle is not available. We also prove that, in Euclidean space, the only closed immersed self-expanding solitons to the weighted generalized inverse curvature flow of codimension one are round hyperspheres.

原文 English 597-616 20 Mathematical Research Letters 25 2 https://doi.org/10.4310/MRL.2018.v25.n2.a13 Published - 2018

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