# Min-Max theory and the Willmore conjecture

@article{Marques2012MinMaxTA, title={Min-Max theory and the Willmore conjecture}, author={Fernando Cod{\'a} Marques and Andre' Neves}, journal={arXiv: Differential Geometry}, year={2012} }

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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