Min-Max theory and the Willmore conjecture

Details Min-Max theory and the Willmore conjecture Min-Max theory and the Willmore conjecture

2012-02-27

arxiv.org/abs/1202.6036v1

Mathematics

Differential Geometry

95 pages

Scientific paper

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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