论文标题
具有非负RICCI曲率和几乎最大局部倒带量的开放流形的有限拓扑类型定理
A finite Topological Type Theorem for open manifolds with Non-negative Ricci Curvature and Almost Maximal Local Rewinding Volume
论文作者
论文摘要
在本文中，我们在几乎最大的局部倒带体积下，提出了具有非负RICCI曲率的开放流形的有限拓扑类型定理。与以前的相关研究不同，我们的定理消除了截面曲率或共轭半径的限制，这在先前结果中是对度量规则性的至关重要的额外假设。值得注意的是，我们的设置不一定满足Toponogov类型的三角比较。实际上，我们采用的方法也扩展到许多以前的相关研究。
In this paper, we present finite topological type theorems for open manifolds with non-negative Ricci curvature, under almost maximal local rewinding volume. Unlike previous related research, our theorems remove the constraints of sectional curvature or conjugate radius, which were crucial additional assumptions on metric regularity in prior results. Notably, our settings do not necessarily satisfy a triangle comparison of Toponogov type. In fact, the method we adopt also extends to many previous related studies.
