Event № 1529
Event № 1529
Type: Lecture
Name: ANALYSIS SEMINAR
Title: Convexity and Teichm\"{u}ller spaces
Speaker: Prof. S. Krushkal
Place:
2nd floor Colloquium Room, Building 216 , Bar Ilan University
Abstract:
We provide restricted negative answers to the Royden-Sullivan problemWe provide restricted negative answers to the Royden-Sullivan problem whether any Teichm\"{u}ller space of dimension greater than $1$ is biholomorphically equivalent to bounded domain in a complex Banach space. The only known result here is Tukia's theorem of 1977 that there is a real analytic homeomorphism of the universal Teichm\"{u}ller space onto a convex domain in some Banach space. We prove: (a) Any Teichm\"{u}ller space $\mathbf T(0,n)$ of the punctured spheres (the surfaces of genus zero) with sufficiently large number of punctures $(n \ge n_0 > 4)$ cannot be mapped biholomorphically onto a bounded convex domain in $\mathbf C^{n-3}$. (b) The universal Teichm\"{u}ller space is not biholomorphically equivalent to a bounded convex domain in uniformly convex Banach space, in particular, to convex domain in the Hilbert space. The proofs involve the existence of conformally rigid domains established by Thurston and some interpolation results for bounded univalent functions.
SubmittedBy:
Elijah Liflyand , liflyand@gmail.com
EventLink: Event № 1529