Min-Max theory and the Willmore conjecture

Abstract

In 1965, T. J. Willmore conjectured that the integral of the square of the mean curvature of a torus immersed in $\mathbb{R}^3$ is at least $2\pi^2$. We prove this conjecture using the min-max theory of minimal surfaces.

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      AUTHOR = {Ros, Antonio},
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      VENUE={{B}ilbao, 2000},
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Authors

Fernando C. Marques

IMPA, Rio de Janeiro, Brazil

André Neves

Imperial College London, South Kensington Campus, London, UK