An Extension of Hsiung–Minkowski Formulas and Some Applications

Research output: Contribution to journalArticle

5 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

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Hypersurface
Eigenvalue Estimates
Mean Curvature
Submanifolds
Riemannian Manifold
Corollary
Curvature
Upper bound
Closed
Generalization

All Science Journal Classification (ASJC) codes

  • Geometry and Topology

Cite this

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An Extension of Hsiung–Minkowski Formulas and Some Applications. / Kwong, Kwok Kun.

In: Journal of Geometric Analysis, Vol. 26, No. 1, 01.01.2016, p. 1-23.

Research output: Contribution to journalArticle

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