报告题目：Gehring-Hayman inequality for quasigeodesics in Banach spaces and its applications

报告人： 王仙桃教授 （湖南师范大学）

报告时间：2024年1月11日（周四）下午 3：30 - 4：30

报告地点：数理楼235

报告摘要: Suppose that E is a Banach space with dimension at least 2, D and D* denote proper subdomains in E, and f stands for a coarsely quasihyperbolic homeomorphism from D to D*. The main purpose of this paper is to establish the following result: If D* is a uniform domain, then the quasigeodesic in D essentially minimizes the length among all arcs in D with the same end-points, up to a universal multiplicative constant. This result gives affirmative answers to the related open problems raised by Heinonen and Rohde from 1993 and by Vaisala from 2005. As the first application, we obtain that the length of the image of a quasigeodesic in D under f minimizes the length among the images of all arcs in D whose end-points are the same as the given quasigeodesic, up to a universal multiplicative constant. As the second application, we show that D being John implies D being inner uniform. This is a generalization of the related result obtained by Kim and Langmeyer in 1998 since this result implies that the assumption of “each quasihyperbolic geodesic in a John domain being a cone arc” in Kim-Langmeyer’s result is redundant.

简介：王仙桃，湖南师范大学教授、博士生导师；教育部新世纪优秀人才计划入选者。国家级双语教学示范课程（数学分析，2009年）和国家级一流本科课程（数学分析，2023年）负责人。研究方向为几何函数论，已在Adv. Math.、Math. Ann.、IMRN等学术刊物发表论文多篇。