A Note on the Geometry of Positively-Curved Riemannian Manifolds
Metric Geometry
2013-12-04 v1
Abstract
In this paper I present a comparison theorem for the waist of Riemannian manifolds with positive sectional curvature. The main theorem of this paper gives a partial positive answer to a conjecture formulated by M.Gromov in [8]. The content of this paper combines two aspects: classical volume comparison theorems of Riemannian geometry, and geometric measure theoretic ideas stemming from Almgren-Pitts Min-Max theory
Keywords
Cite
@article{arxiv.1312.0792,
title = {A Note on the Geometry of Positively-Curved Riemannian Manifolds},
author = {Yashar Memarian},
journal= {arXiv preprint arXiv:1312.0792},
year = {2013}
}
Comments
20 pages, 1 figure