论文标题
保留度量度量空间等轴测值组
The Measure Preserving Isometry Groups of Metric Measure Spaces
论文作者
论文摘要
Bochner的定理说，如果$ m $是一个紧凑的Riemannian歧管，则具有负RICCI曲率，那么Isometry $ \ operatatRatorName {iso}（m）$是有限的。在本文中，我们表明，如果$（x，d，m）$是一个紧凑的度量度量空间，则具有统一的ricci曲率，那么在Sturm的意义上，保留等轴测组$ \ operatorator $ \ operatorName {iso}（x，x，d，m）$是有限的。我们还对紧凑的加权riemannian歧管和负面的bakry-émeryricci曲率的措施保持等轴测组的量度进行有效估计，除了小部分。
Bochner's theorem says that if $M$ is a compact Riemannian manifold with negative Ricci curvature, then the isometry group $\operatorname{Iso}(M)$ is finite. In this article, we show that if $(X,d,m)$ is a compact metric measure space with synthetic negative Ricci curvature in Sturm's sense, then the measure preserving isometry group $\operatorname{Iso}(X,d,m)$ is finite. We also give an effective estimate on the order of the measure preserving isometry group for a compact weighted Riemannian manifold with negative Bakry-Émery Ricci curvature except for small portions.
