Abstract
In 1965, T. J. Willmore conjectured that the integral of the square of the mean curvature of a torus immersed in $\mathbb{R}^3$ is at least $2\pi^2$. We prove this conjecture using the min-max theory of minimal surfaces.
In 1965, T. J. Willmore conjectured that the integral of the square of the mean curvature of a torus immersed in $\mathbb{R}^3$ is at least $2\pi^2$. We prove this conjecture using the min-max theory of minimal surfaces.
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