Mean Convex Smoothing of Mean Convex Cones
Differential Geometry
2022-02-17 v1 Analysis of PDEs
Abstract
We show that any minimizing hypercone can be perturbed into one side to a properly embedded smooth minimizing hypersurface in the Euclidean space, and every viscosity mean convex cone admits a properly embedded smooth mean convex self-expander asymptotic to it near infinity. These two together confirm a conjecture of Lawson \cite[Problem 5.7]{Brothers86_OpenProblems}.
Keywords
Cite
@article{arxiv.2202.07851,
title = {Mean Convex Smoothing of Mean Convex Cones},
author = {Zhihan Wang},
journal= {arXiv preprint arXiv:2202.07851},
year = {2022}
}
Comments
27 pages; Comments are welcome