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 language | English |
---|---|
Pages (from-to) | 1-23 |
Number of pages | 23 |
Journal | Journal of Geometric Analysis |
Volume | 26 |
Issue number | 1 |
DOIs | |
Publication status | Published - 2016 Jan 1 |
All Science Journal Classification (ASJC) codes
- Geometry and Topology