论文标题
非负RICCI曲率和逃生率差距
Nonnegative Ricci curvature and escape rate gap
论文作者
论文摘要
让$ m $为非负RICCI曲率的开放$ n $ n $ manifold，让$ p \在m $中。我们表明，如果$（m，p）$比某些正常数$ε（n）$要小，也就是说，最小代表$π_1（m，p）$的地理环路（m，p）$从任何有限的球中逃脱，以相对于其长度的线性较小，则几乎是$π_1（m，p）$。这概括了作者以前的工作，其中考虑了零逃逸率。
Let $M$ be an open $n$-manifold of nonnegative Ricci curvature and let $p\in M$. We show that if $(M,p)$ has escape rate less than some positive constant $ε(n)$, that is, minimal representing geodesic loops of $π_1(M,p)$ escape from any bounded balls at a small linear rate with respect to their lengths, then $π_1(M,p)$ is virtually abelian. This generalizes the author's previous work, where the zero escape rate is considered.
