On Area Comparison and Rigidity Involving the Scalar Curvature
Differential Geometry
2013-09-05 v1
Abstract
We prove a splitting theorem for Riemannian n-manifolds with scalar curvature bounded below by a negative constant and containing certain area-minimising hypersurfaces (Theorem 3). Thus we generalise [25,Theorem 3] by Nunes. This splitting result follows from an area comparison theorem for hypersurfaces with non-positive Sigma-constant (Theorem 4) that generalises [23, Theorem 2]. Finally, we will address the optimality of these comparison and splitting results by explicitly constructing several examples.
Keywords
Cite
@article{arxiv.1309.1050,
title = {On Area Comparison and Rigidity Involving the Scalar Curvature},
author = {Vlad Moraru},
journal= {arXiv preprint arXiv:1309.1050},
year = {2013}
}