论文标题
受YAU刚度理论启发的任意编成均值曲率流的新发展
New Developments in Mean Curvature Flow of Arbitrary Codimension Inspired By Yau Rigidity Theory
论文作者
论文摘要
在这项调查中，我们将重点介绍具有球体定理的平均曲率流理论，并讨论有关受亚序列的YAU刚度理论启发的关于融合定理的最新发展。作为平均曲率流的收敛定理的后果，获得了几个新的可用于亚频率的可区分定理。应该强调的是，定理4.1是任意编成的平均曲率流的最佳收敛定理，这意味着具有正RICCI曲率的Submanifolds的第一个最佳可分解球定理。最后，我们列出了该领域未解决的问题的列表。
In this survey, we will focus on the mean curvature flow theory with sphere theorems, and discuss the recent developments on the convergence theorems for the mean curvature flow of arbitrary codimension inspired by the Yau rigidity theory of submanifolds. Several new differentiable sphere theorems for submanifolds are obtained as consequences of the convergence theorems for the mean curvature flow. It should be emphasized that Theorem 4.1 is an optimal convergence theorem for the mean curvature flow of arbitrary codimension, which implies the first optimal differentiable sphere theorem for submanifolds with positive Ricci curvature. Finally, we present a list of unsolved problems in this area.
