论文标题
RICCI流量的稳定长度函数
A steady length function for Ricci flow
论文作者
论文摘要
RICCI流动奇异性分析的基本步骤是Perelman发现单调体积数量的发现，该数量检测到（Arxiv：Math/0211159）中的孤子。 Feldman，Ilmanen和NI在2005年发现了类似的数量，这些数量检测到了孤子的扩大。当前的工作将修改的长度引入了朝着稳定的单调公式的第一步。该长度的功能以通常的方式生成距离函数，该距离函数可满足几种差分不平等，这些不平等现象精确地饱和，以满足稳定孤子方程的修改。
A fundamental step in the analysis of singularities of Ricci flow was the discovery by Perelman of a monotonic volume quantity which detected shrinking solitons in (arXiv:math/0211159). A similar quantity was found by Feldman, Ilmanen, and Ni in 2005 which detected expanding solitons. The current work introduces a modified length functional as a first step towards a steady soliton monotonicity formula. This length functional generates a distance function in the usual way which is shown to satisfy several differential inequalities which saturate precisely on manifolds satisfying a modification of the steady soliton equation.
