Min-Max theory and the Willmore conjecture
Differential Geometry
2013-03-29 v2 Analysis of PDEs
Geometric Topology
Abstract
In 1965, T. J. Willmore conjectured that the integral of the square of the mean curvature of a torus immersed in Euclidean three-space is at least 2\pi^2. We prove this conjecture using the min-max theory of minimal surfaces.
Cite
@article{arxiv.1202.6036,
title = {Min-Max theory and the Willmore conjecture},
author = {Fernando C. Marques and André Neves},
journal= {arXiv preprint arXiv:1202.6036},
year = {2013}
}
Comments
96 pages. Revised version. To appear in Annals of Mathematics