Title:Harmonic Extensions of Weil–Petersson Circle Homeomorphisms

Speaker:Abderrahim Mesbah(postdoctoral researcher)

Time:  June 25,  2026, 10:00-11:30

Venue: Room 3A02, Building No. 37, Wushan Campus

Abstract: 

Harmonic maps play a central role in Teichmüller theory. It was conjectured by Schoen and proved by Marković 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 Kähler 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.