10-07【戴 嵩】腾讯会议 几何拓扑及高阶Teichmuller研讨班系列报告之三

发布者:万宏艳发布时间:2022-09-30浏览次数:361

报告题目:Bounded differentials on unit disk and the associated geometry


报告人:戴嵩,天津大学应用数学中心


时间: 2022年10月7日(周五)14:30-15:30


腾讯会议:647-4448-8711 


点击链接入会,或添加至会议列表:

https://meeting.tencent.com/dm/VvMCGE4fgWA0


摘要:Let D be the unit disk with hyperbolic metric. Given a holomorphic quadratic differential q, there is a harmonic map f from D to itself such that q is the Hopf differential. Under certain completeness condition, Wan showed that q is bounded (with respect to the hyperbolic metric) is equivalent to either the energy density is bounded or f is quasi-conformal. In this talk, we study more holomorphic differentials and the associated geometries. For holomorphic cubic, quartic and sextic differentials, the associated geometries are hyperbolic affine spheres in R^3, maximal surfaces in H^{2,n} and J-holomorphic curves in H^{4,2}. Combining Wan's PDE approach and Higgs bundle techniques, we show that under the completeness condition, the holomorphic differential is bounded is equivalent to either the induced metric is mutually bounded with the hyperbolic metric or the curvature of the induced metric is bounded above by a negative constant. We also generalize Wan’s result from the single equation to the equation system, which relates to the Toda system and the Hitchin equation in the non-Abelian Hodge theory. This is a joint work with Qiongling Li.  


“几何拓扑及高阶Teichmuller研讨班”将邀请本领域与几何、拓扑、分析、代数、概率、动力系统等相关的专家给1至1.5小时的报告。前半个小时的报告将概括研究方向的内容,面向本科生、研究生以及相关的专家,以引起大家的兴趣,深入学术交流。