学术报告报告主题: Harmonic Extensions of Weil–Petersson Circle Homeomorphisms
报 告 人: Abderrahim Mesbah
报告时间： 2026 年 6 月 25 日（星期四）上午 10:00-11:30
报告地点： 37 号楼 3A02
邀 请 人: 陈麒羽、钟友良 副教授
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2026 年 6 月 22 日
报告摘要：
Harmonic maps play a central role in Teichmüller theory. It was conjectured by Schoen and proved by Markovi? that every quasisymmetric homeomorphism of the circle admits a quasiconformal harmonic extension to the disk. Together with related works, notably by Li–Tam and Wan, this yields a parametrization of the universal Teichmüller space in terms of bounded holomorphic quadratic differentials. On the other hand, the Weil–Petersson Teichmüller space forms an important subspace of the universal Teichmüller space which is equipped with a natural complete K?hler structure, and has been extensively studied in recent years. In this talk, we study Weil–Petersson circle homeomorphisms via quasiconformal harmonic maps. We show in particular that square-integrable holomorphic quadratic differentials parametrize the Weil–Petersson Teichmüller space, and that the anti-holomorphic energy of the harmonic extension satisfies a suitable energy-minimizing property among quasiconformal extensions.
报告人介绍：
Abderrahim Mesbah is a postdoctoral researcher at the Beijing Institute of Mathematical Sciences and Applications (BIMSA). He obtained his Ph. D in 2024 from University of Luxembourgunder the supervision of Prof. Jean-Marc Schlenker. His research focuses on convex 3-manifolds, in particular on quasi-Fuchsian manifolds and globally hyperbolic 3-manifolds, with related resultspublished in J. Geom. Anal., J. Topol., Bull. Lond. Math. Soc., etc.