mm-空间到具有加倍测度空间的可观测集中
Observable concentration of mm-spaces into spaces with doubling measures
摘要：
测度集中的性质是mm-空间$X$上的任意1-Lipschitz函数$f:X\to \mathbb{R}$几乎接近于一个常数函数.本文证明了，如果出现这种集中现象，则从$X$到具有加倍测度的空间$Y$的任何1-Lipschitz映射$f$也集中到常数映射.作为推论，我们得到了到黎曼流形且具有里奇曲率下界的1-Lipschitz映射也集中于常数映射.
英文摘要：
The property of measure concentration is that an arbitrary 1-Lipschitz function $f:X\to \mathbb{R}$ on an mm-space $X$ is almost close to a constant function. In this paper, we prove that if such a concentration phenomenon arise, then any 1-Lipschitz map $f$ from $X$ to a space $Y$ with a doubling measure also concentrates to a constant map. As a corollary, we get any 1-Lipschitz map to a Riemannian manifold with a lower Ricci curvature bounds also concentrates to a constant map.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
