NewEvery arXiv paper, its researchers & institutions — mapped.
paper

Min-Max theory and the Willmore conjecture

arXiv:1202.6036

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 2π^2. We prove this conjecture using the min-max theory of minimal surfaces.

96 pages. Revised version. To appear in Annals of Mathematics