Min-Max theory and the Willmore conjecture
  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. 
Fernando C. Marques and Andr\'e Neves
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