Min-Max theory and the Willmore conjecture

Fernando C. Marques; André Neves

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arXiv · 1202.6036

Min-Max theory and the Willmore conjecture

Fernando C. Marques·André Neves

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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.

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Fernando C. Marques, André Neves. 2012-02-27. Min-Max theory and the Willmore conjecture. https://arxiv.org/abs/1202.6036

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