# 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}
}
• Published 2012
• Mathematics
• arXiv: Differential Geometry
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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