论文标题
RICCI边界较低的非倒塌空间上的渐近等级法
Asymptotic isoperimetry on non collapsed spaces with lower Ricci bounds
论文作者
论文摘要
本文研究了针对$ n $ dimensional $ {\ rm rm rcd}（k，n）$ spaces $（x，x，x，x，x，mathsf {d}，\ mathscr {\ mathscr {hh h} n）$ sharp and Corgid iSoperimetric比较定理和渐近等级的差异等。此外，我们获得了几乎定理的定理，该定理是根据数字概况和增强的后果在几种功能不平等的水平上提高的。即使在平滑，非紧凑的歧管的经典环境中，我们的大多数陈述都是新的，而RICCI曲率范围较低。合成理论通过紧凑和稳定性参数起着关键作用。
This paper studies sharp and rigid isoperimetric comparison theorems and asymptotic isoperimetric properties for small and large volumes on $N$-dimensional ${\rm RCD}(K,N)$ spaces $(X,\mathsf{d},\mathscr{H}^N)$. Moreover, we obtain almost regularity theorems formulated in terms of the isoperimetric profile and enhanced consequences at the level of several functional inequalities. Most of our statements are new even in the classical setting of smooth, non compact manifolds with lower Ricci curvature bounds. The synthetic theory plays a key role via compactness and stability arguments.
