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Title: | 探討由最小-最大定理證明威爾莫猜想 A survey on proof of Willmore conjecture by min-max theory |
Authors: | Shu-Ming Liu 劉書銘 |
Advisor: | 張樹城 |
Keyword: | 威爾莫猜想,最小最大定理,極小曲面, Willmore conjecture,min-max theory,minimal surface, |
Publication Year : | 2014 |
Degree: | 碩士 |
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. |
URI: | http://tdr.lib.ntu.edu.tw/jspui/handle/123456789/16704 |
Fulltext Rights: | 未授權 |
Appears in Collections: | 數學系 |
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ntu-103-1.pdf Restricted Access | 2.02 MB | Adobe PDF |
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