个人简介：

王仙桃，湖南省首批二级教授，教育部新世纪优秀人才计划入选者，湖南省新世纪121第二层次人选，湖南省杰出青年基金获得者，湖南省学科带头人；湖南省十二五重点学科数学、湖南省首届普通高校科技创新团队、湖南省普通高校教学团队的带头人，国家级双语教学示范课程主持人。

研究领域：

主要为Klein群、拟共形映射以及调和映射，解决了发表在国际数学最权威刊物Acta.Math.上悬而未决达三十多年的问题，在Adv. Math., Math. Ann., IMRN等刊物发表论文80多篇。

报告题目：Gehring-Hayman inequality forquasigeodesics in Banach spaces and its application

摘要：Let E be a Banach space withdiam(E)>(or =)2, D a propersubdomain in E, and f:D\to D' a coarsely quasihyperbolic homeomorphism. Themain purpose of this paper is to establish the following result: If D'is a uniform domain, then the quasigeodesic in D essentiallyminimizes 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 problemsraised by Heinonen and Rohde from 1993 and by Vaisalafrom2005.

As the first application, we obtain that the length of the image of aquasigeodesic

in Dunder fminimizes 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 ageneralization 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 inR^nbeing a cone arc" is redundant.