An extension of Hsiung-Minkowski formulas and its applications
Differential Geometry
2014-07-17 v2
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 eigenvalue estimates for hypersurfaces.
Keywords
Cite
@article{arxiv.1307.3025,
title = {An extension of Hsiung-Minkowski formulas and its applications},
author = {Kwok-Kun Kwong},
journal= {arXiv preprint arXiv:1307.3025},
year = {2014}
}
Comments
Typos corrected and references updated. To appear in Journal of Geometric Analysis