【学术报告】Planar Sobolev extension domains and quasiconformal mappings

• 主讲人：Yi Zhang
• 时间：Dec. 2, 2021 21:00-22:00 Beijing time (16:00-17:00 St Petersburg time)
• 地点：online

Abstract: In 1979, Goldshtein et al. pointed out that a bounded simply connected planar domain is a W^{1,\,2}-extension domain if and only if it is a quasidisk. This result was later generalized by Jone to all dimensions, showing that uniform domains are W^{1,\,p}-extension domain for any 1\le p<\infty. However, there are simply connected W^{1,\,p}-extension domains in the plane which are not uniform when p\neq 2, pointed out by e.g. Maz'ya. In this talk I will present my joint work with Koskela and Rajala on this problem, and show its connection to the Ahlfors' quasiconformal reflection theorem.  

 

Bio: My main background is in complex analysis and geometric function theory. I have also done works on harmonic analysis, functional analysis, nonlinear elliptic partial differential equations (p-Laplacians and infinity Laplacian), free boundary problems, calculus of variations, eigenvalue problems of p-Laplacians and so on. Especially, I am interested in problems in the intersection of analysis and geometry.

B.S., Math & Applied Math, Beihang University, September 1, 2009 – June 30, 2013.

M.S., Mathematics, University of Jyväskylä (Supervisor: Pekka Koskela), August 1, 2013 – July 30, 2014.

Ph.D., Mathematics, University of Jyväskylä (Supervisor: Pekka Koskela), August 1, 2014 – July 30, 2017.

Doctoral Dissertation: Planar Sobolev extension domains. (Defended on May 5th, 2017)