一、报告题目：Almost Lipschitz homeomorphisms of Banach spaces and spheres

二、报告人： 程庆进 教授

三、时 间：2026年5月11日（周一）15:00--16:00

四、腾讯会议：489-426-320

报告摘要：In this talk, In this talk, we investigate a notion that is slightly weaker than the Lipschitz homeomorphism, namely the almost Lipschitz homeomorphism. Roughly speaking, the Lipschitz assumptions are weakened by introducing powers of a logarithmic factor.  We first present the basic lifting method  of almost Lipschitz homeomorphisms, and then combine this method with Lipschitz-free spaces to generate  three pairs of separable Banach spaces that are almost Lipschitz but not Lipschitz homeomorphic.

On the other hand, we also employ the notion  to study the classification of spheres. Let $1\leq p,q<\infty$. Then any two different unit spheres of $L_p$ spaces are not almost Lipschitz homeomorphic. This is done by using Hamming concentration inequality and by establishing a sphere version of the Gorelik principle and the approximate midpoint method.

报告人简介：程庆进，厦门大学数学科学学院教授，博士生导师。主持多项国家自然科学基金面上项目，并参加一项国家自然科学基金重点项目。在J. Convex Anal.、J. Funct. Anal.、Studia Math.、Sci. China Ser. A等国际期刊上发表SCI学术论文30多篇。

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