开三角形的Toponogov比较定理
Toponogov comparison theorem for open triangles
摘要：
献给Gromoll教授：本文的目的是将Toponogov比较定理推广到具有光滑凸边界的完备黎曼流形。一个测地三角形将被一个站在流形边界上的开（测地）三角形代替，一个模型曲面将被一个具有全测地边界的旋转圆柱的万有覆盖面代替。我们的定理的应用可以在我们的文章“Applications of Toponogov's comparison theories for open triangles”（arXiv：1102.4156）中找到。
英文摘要：
Dedicated to Professor Gromoll: The aim of our article is to generalize the Toponogov comparison theorem to a complete Riemannian manifold with smooth convex boundary. A geodesic triangle will be replaced by an open (geodesic) triangle standing on the boundary of the manifold, and a model surface will be replaced by the universal covering surface of a cylinder of revolution with totally geodesic boundary. Applications of our theorem are found in our article "Applications of Toponogov's comparison theorems for open triangles" (arXiv:1102.4156).
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。
