An Extension of Hsiung–Minkowski Formulas and Some Applications

Kwok Kun Kwong

Research output: Contribution to journalArticlepeer-review

18 Citations (Scopus)

Abstract

We prove a generalization of Hsiung–Minkowski formulas for closed submanifolds in semi-Riemannian manifolds with constant curvature. As a corollary, we obtain volume and area upper bounds for k-convex hypersurfaces in terms of a weighted total k-th mean curvature of the hypersurface. We also obtain some Alexandrov-type results and some eigenvalue estimates for hypersurfaces.

Original languageEnglish
Pages (from-to)1-23
Number of pages23
JournalJournal of Geometric Analysis
Volume26
Issue number1
DOIs
Publication statusPublished - 2016 Jan 1

All Science Journal Classification (ASJC) codes

  • Geometry and Topology

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