Title: Horoboundaries of coarsely convex spaces Show Chinese title

Title: 粗凸空间的Horoboundary

Abstract: A horoboundary is one of the attempts to compactify metric spaces, and is constructed using continuous functions on metric spaces. It is a concept that includes global information of metric spaces, and its correspondence with an ideal boundary constructed using geodesics has been studied in nonpositive curvature spaces such as CAT(0) spaces and geodesic Gromov hyperbolic spaces. We will introduce a certain correspondence between the horoboundary and the ideal boundary of coarsely convex spaces, which can be regarded as a generalization of spaces of nonpositive curvature. Show Chinese abstract

Abstract: 一个悬球边界是尝试对度量空间进行紧化的一种方法，它是通过度量空间上的连续函数构造的。 它是一个包含度量空间全局信息的概念，并且其与通过测地线构造的理想边界之间的对应关系已在非正曲率空间（如CAT(0)空间和测地线Gromov双曲空间）中进行了研究。 我们将介绍粗凸空间的悬球边界与理想边界之间的一种特定对应关系，这可以被视为非正曲率空间的一种推广。