Min-Max theory and the Willmore conjecture

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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 R3 is at least 2π2. We prove this conjecture using the min-max theory of minimal surfaces. © 2014 Department of Mathematics, Princeton University.

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Marques, F. C., & Neves, A. (2014). Min-Max theory and the Willmore conjecture. Annals of Mathematics, 179(2), 683–782. https://doi.org/10.4007/annals.2014.179.2.6

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