Min-Max theory and the Willmore conjecture

Fernando C. Marques; André Neves

doi:10.4007/annals.2014.179.2.6

Min-Max theory and the Willmore conjecture

Fernando C. Marques, André Neves

Research output: Contribution to journal › Article › peer-review

310 Scopus citations

Abstract

In 1965, T. J. Willmore conjectured that the integral of the square of the mean curvature of a torus immersed in R³ is at least 2π². We prove this conjecture using the min-max theory of minimal surfaces.

Original language	English (US)
Pages (from-to)	683-782
Number of pages	100
Journal	Annals of Mathematics
Volume	179
Issue number	2
DOIs	https://doi.org/10.4007/annals.2014.179.2.6
State	Published - Mar 2014
Externally published	Yes

All Science Journal Classification (ASJC) codes

Statistics and Probability
Statistics, Probability and Uncertainty

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10.4007/annals.2014.179.2.6

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title = "Min-Max theory and the Willmore conjecture",

abstract = "In 1965, T. J. Willmore conjectured that the integral of the square of the mean curvature of a torus immersed in R3 is at least 2π2. We prove this conjecture using the min-max theory of minimal surfaces.",

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Min-Max theory and the Willmore conjecture

Abstract

All Science Journal Classification (ASJC) codes

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