A sharp bound for the area of minimal surfaces in the unit ball
Differential Geometry
2012-01-11 v2
Abstract
Let \Sigma be a k-dimensional minimal surface in the unit ball B^n which meets the unit sphere orthogonally. We show that the area of \Sigma is bounded from below by the volume of the unit ball in R^k. This answers a question posed by R. Schoen.
Cite
@article{arxiv.1108.4544,
title = {A sharp bound for the area of minimal surfaces in the unit ball},
author = {S. Brendle},
journal= {arXiv preprint arXiv:1108.4544},
year = {2012}
}
Comments
To appear in Geometric and Functional Analysis