Sharp Lower Bounds on Density of Area-Minimizing Cones
Differential Geometry
2016-02-22 v2
Abstract
We prove that the density of a topologically nontrivial, area-minimizing hypercone with an isolated singularity must be greater than the square root of 2. The Simons' cones show that this is the best possible constant. If one of the components of the complement of the cone has nontrivial kth homotopy group, we prove a better bound in terms of k; that bound is also best possible. The proofs use mean curvature flow.
Cite
@article{arxiv.1010.5068,
title = {Sharp Lower Bounds on Density of Area-Minimizing Cones},
author = {Tom Ilmanen and Brian White},
journal= {arXiv preprint arXiv:1010.5068},
year = {2016}
}
Comments
13 pages. In the new version (May 12, 2013), we have added an appendix that summarizes the main facts about mean curvature flow used in the proofs