Bourbaki研讨会1081：最小-最大方法和Willmore猜想，在Fernando Codá Marques和André Arroja Neves之后
Bourbaki Seminar 1081 : Min-max methods and the Willmore conjecture, after Fernando Codá Marques and André Arroja Neves
摘要：
两年前，FC马克斯和A.A. Neves在三维球的封闭可求长二维流的框架内实现了几何测度论中的极小-极大方法，这是由于F。Almgren和J. Pitts。使用这种方法，他们成功地证明了著名的克利福德环面最小化所有非零亏格在$S^3$的封闭极小曲面之间的面积。他们的工作的另一个引人注目的结果是提供了Willmore猜想的证明。这次谈话的目的是讨论第一的一般框架，这两个定理的马克斯和内维斯。然后，我们将介绍其证明的结构和一些关键细节。然后，我们将解决这个显着的贡献微积分的范围内的表面上的变化在一个3维空间。
英文摘要：
Two years ago, F.C. Marques and A.A. Neves implemented, in the framework of closed rectifiable 2-dimensional currents of the 3-dimensional sphere, a min-max method in geometric measure theory due to F. Almgren and J. Pitts. Using this approach they succeeded in proving that the famous Clifford torus minimizes the area among all closed minimal surfaces of non-zero genus in $S^3$. Another spectacular consequence of their work is to provide a proof of the Willmore conjecture. The goal of this talk is to discuss first the general framework of these two theorems of Marques and Neves. We shall then present the structures and some key details of their proofs. We will then address the scope of this remarkable contribution to the calculus of variations on surfaces in a 3-dimensional space.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
