推廣威爾莫流的一個明顯解

Abstract

本篇文章中我們造了一個推廣威爾莫流的明顯解。我們可以證明在3維的歐幾里德空間中找到一個橢球的例子，在一開始時間為零的橢球為初始曲面有很大的威爾莫能量使得它所滿足的推廣威爾莫流對所有時間皆平滑的存在，而且當時間逼近無限大將收斂到一個圓球。

In this thesis we construct an explicit solution of the generalized Willmore flow. As an application, we show that there exists an ellipsoid M in the 3-dimensional Euclidean space which has large Willmore energy such that the generalized Willmore flow with M0 as the initial surface exists smoothly for all times and converges to a round sphere as the time tends to infinity.