关于局部诺伊曼等周常数

On the Local Neumann Isoperimetric Constant

本文引入流形中一个相对区域上的相对等周不等式,并说明它等价于相对Sobolev不等式.在倍体积假设条件下,推出了度量球上的经典等周不等式.最后,讨论了该不等式在一些曲率条件下的应用和凯勒—里奇流中的应用.

We introduce a relative isoperimetric inequality for relative domains on a manifold and show its equivalence to the relative Sobolev inequality.Together with the volume doubling condition it implies the classical isoperimetric inequality on a metric ball.Application to several curvature conditions as well as K?hler-Ricci flow will be discussed.