Alexandrov空间灵魂的注入半径
The Injectivity Radius of Souls of Alexandrov Spaces
AI总结：
本文将Šarafutdinov关于非紧非负曲率黎曼流形注入半径的下界推广到Alexandrov空间，证明当空间注入半径不等于其灵魂的注入半径时，其至少为$πK^{-1/2}$，并系统引入灵魂概念及比较两种注入半径定义。
摘要：
关于非紧非负曲率黎曼流形中涉及灵魂的注入半径的尖锐下界，可追溯至Šarafutdinov。我们将该下界推广到Alexandrov空间的情形。我们的主要定理如下：若非负曲率Alexandrov空间的注入半径与其灵魂的注入半径不一致，则它至少为$πK^{-1/2}$，其中$K$是上曲率界。我们较详细地引入Alexandrov空间的灵魂，并比较两种注入半径的概念。
英文摘要：
A sharp lower bound for the injectivity radius in noncompact nonnegatively curved Riemannian manifolds involving their soul goes back to Šarafutdinov. We generalize this bound to the setting of Alexandrov spaces. Our main theorem reads as follows. If the injectivity radius of an Alexandrov space of nonnegative curvature does not coincide with the one of its souls, then it is at least $ πK^{-1/2} $, where $ K $ is an upper curvature bound. We introduce the soul of Alexandrov spaces in some detail and compare two notions of injectivity radii.
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。
