报告题目：Moduli of ring domains and univalent harmonic mappings

报告人：广东以色列理工学院Antti Rasila 副教授

报告时间：2022年6月21日14:30-15:30

报告地点：数统院会议室

邀请人：李佩瑾

报告摘要：Two doubly connected domains D and D∗ are conformally equivalent if, and only if, they have the same moduli. This, however, needs not be true if D and D* are harmonically equivalent, that is, if there exists a harmonic homeomorphism from D onto D∗. For example, the harmonic mapping f(z) = (z+1/z)/2 maps the annulus 1<|z|<R onto the annulus 1<|z|<(R+1/R)/2. This question led the 1962 famous conjecture of Nitsche. This long-standing conjecture was settled affirmatively by Iwaniec, Kovalev, and Onninen. The same authors also asked the following more general question: Question: Characterize pairs (D,D*) of doubly connected domains that admit a univalent harmonic mapping from D onto D*. In this presentation, we investigate this question for Teichmüller type domeans T(s), T(t), where s,t>1. This presentation is based on joint work with Bshouty, Lyzzaik and Vasudevarao.

报告人简介：Antti Rasila，广东以色列理工学院副教授。主要研究方向为复分析，特别是拟共形映射和调和映射。主持国家自然科学基金面上项目1项，发表论文60多篇，出版专著2本，是多个国际杂志的评审和主编。在《Adv. Math.》、《Calc. Var. Partial Differential Equations》、《Math. Z.》、《SIAM J. Sci. Comput.》等国内外数学杂志发表学术论文60余篇。