The isoperimetric inequality for a minimal submanifold in Euclidean space
Differential Geometry
2020-10-07 v4 Analysis of PDEs
Abstract
We prove a Sobolev inequality which holds on submanifolds in Euclidean space of arbitrary dimension and codimension. This inequality is sharp if the codimension is at most 2. As a special case, we obtain a sharp isoperimetric inequality for minimal submanifolds in Euclidean space of codimension at most 2.
Keywords
Cite
@article{arxiv.1907.09446,
title = {The isoperimetric inequality for a minimal submanifold in Euclidean space},
author = {S. Brendle},
journal= {arXiv preprint arXiv:1907.09446},
year = {2020}
}
Comments
final version, to appear in J Amer Math Soc