Min-Max theory and the Willmore conjecture

• 成果类型: Article
• 署名作者: Marques, Fernando C.; Neves, Andre
• 刊物名称: ANNALS OF MATHEMATICS
• ISSN/ISSBN: 0003-486X
• DOI: 10.4007/annals.2014.179.2.6
• 发表日期: 2014
• 页码: 683-782
• 关键词: minimal-surfaces; mean-curvature; tori; REGULARITY; invariant

摘要

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