论文标题
较低RICCI有界度量的刻有半径界限，具有平均凸边界
Inscribed Radius Bounds for Lower Ricci Bounded Metric Measure Spaces with Mean Convex Boundary
论文作者
论文摘要
考虑具有OHTA和Sturm的量度收缩特性，或者在Lott，Sturm和Villani的意义上具有衡量量的曲率下限，以实质上是非分支的度量测量空间。我们证明了任何子集的铭文半径上的尖锐上限，其边界在其广义平均曲率上具有适当签名的下限。这提供了与Kasue（1983）和Li（2014）结果的非平滑类似物。我们证明了关于这种界限的稳定性语句，并且 - 在Riemannian曲率差异（RCD）设置中 - 表征平等的情况。
Consider an essentially nonbranching metric measure space with the measure contraction property of Ohta and Sturm, or with a Ricci curvature lower bound in the sense of Lott, Sturm and Villani. We prove a sharp upper bound on the inscribed radius of any subset whose boundary has a suitably signed lower bound on its generalized mean curvature. This provides a nonsmooth analog to a result of Kasue (1983) and Li (2014). We prove a stability statement concerning such bounds and - in the Riemannian curvature-dimension (RCD) setting - characterize the cases of equality.
