Weighted Hsiung-Minkowski formulas and rigidity of umbilical hypersurfaces

Kwong Kwok-Kun, Hojoo Lee, Juncheol Pyo

Research output: Contribution to journalArticle

Abstract

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.

Original languageEnglish
Pages (from-to)597-616
Number of pages20
JournalMathematical Research Letters
Volume25
Issue number2
DOIs
Publication statusPublished - 2018 Jan 1

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Rigidity
Hypersurface
Reflection Principle
Curvature Flow
Warped Product
Closed
Hypersphere
Integral Formula
Generalized Inverse
Mean Curvature
Codimension
Euclidean space
Solitons
Higher Order
Class

All Science Journal Classification (ASJC) codes

  • Mathematics(all)

Cite this

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Weighted Hsiung-Minkowski formulas and rigidity of umbilical hypersurfaces. / Kwok-Kun, Kwong; Lee, Hojoo; Pyo, Juncheol.

In: Mathematical Research Letters, Vol. 25, No. 2, 01.01.2018, p. 597-616.

Research output: Contribution to journalArticle

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