局部CAT(<i>k</i>) 空间上的一个Toponogov型比较定理

局部CAT(k) 空间上的一个Toponogov型比较定理

摘要: 探讨了局部Cartan-Alexandrov-Toponogov (CAT(k))空间的Toponogov型比较性质．基于曲率有下界的Alexandrov空间整体化定理，通过推导，获得了局部CAT(k) 空间的Toponogov型比较定理，其可为局部CAT(k) 空间的整体化定理提供证明．

Abstract: The Toponogov-type properties of locally Cartan-Alexandrov-Toponogov (CAT(k)) spaces are studied. Based on the idea of a recent new proof of the globalization theorem for Alexandrov spaces with a lower curvature bound, a Toponogov-type comparison theorem for locally CAT(k) spaces is presented, which implies the globalization theorem for locally CAT(k) spaces.