探討由最小-最大定理證明威爾莫猜想

Abstract

2012年，Fernando C.Marques和Andre Neves所著的論文：Min-max theory and Willmore conjecture成功地證明了1965年由Willmore所提出著名的猜想。他們使用了幾何測度論的方法並且應用Min-max theory給出一個漂亮的證明方法，其中特別的是如何造出能夠使用Min-max theory的canonical family，這個是整篇論文中最重要的部分；我們將會在本文中說明如何造出這樣的canonical family，此外也會將一些Willmore猜想相關的性質附上並且補上他們的證明。

In 2012, the thesis: Min-max theory and Willmore conjecture wrote by Fernando C.Marques and Andre Neves. Which successful proof the well-known Willmore conjecture. They used the method of geometric measure theory and application of Min-max theory gives a nice proof, which is how to create a special ability to use Min-max theory of canonical family, this is the whole thesis is the most important part; we will explain how to create such a canonical family in this article; on the other hand, we will addition to some property of the Willmore conjecture and their proof.