Min-Max theory and the Willmore conjecture

2012/02/27 by Marques, Fernando C., Neves, André · 16 citations
#53A10 #53C42 #Analysis of PDEs (math.AP) #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Topology (math.GT)

paper · doi:10.48550/arxiv.1202.6036

Abstract

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 2π². We prove this conjecture using the min-max theory of minimal surfaces.

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• The Min-Max theory and the Willmore conjecture
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