The Journal of Geometric Analysis

, Volume 26, Issue 1, pp 1–23

An Extension of Hsiung–Minkowski Formulas and Some Applications

Article

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.

Keywords

Hsiung–Minkowski formulas Alexandrov’s theorem Conformal Killing vector fields Eigenvalue estimate 

Mathematics Subject Classification

Primary 53C40 Secondary 53C50 

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Copyright information

© Mathematica Josephina, Inc. 2014

Authors and Affiliations

  1. 1.Department of MathematicsNational Cheng Kung UniversityTainanTaiwan, ROC

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