一类广义Busemann-Petty问题的稳定性

The Stability of a Class of Generalized Busemann-Petty Problem

主要确立了广义Busemann-Petty问题的稳定性;结果涉及了维数限制上的广义Busemann-Petty问题的稳定性以及与广义截面体类结构相关联的Busemann-Petty问题的稳定性;细化并蕴含了Koldobsky和马丹所给出的广义Busemann-Petty问题的稳定性结果,且为进一步深化相关的研究提供了启示.

This paper mainly discusses the stability of generalized Busemann-Petty problem, its results involving in the stability of generalized Busemann-Petty problem on dimension-restriction and the stability of Busemann-Petty problem related to generalized-intersection-like structure. The results in this paper more detailedly segments and contains the stability results of generalized Busemann-Petty problem given by Koldobsky and Ma Dan, providing the enlightenment for deepening the related researches.