A short geometric proof of the Zalcman and Bieberbach conjectures

Abstract

We show that complex geometric features of Teichmuller spaces create explicitly the extremals of generic homogeneous holomorphic functionals on univalent functions. In particular this gives proofs of the well-known Zalcman and Bieberbach conjectures and many new distortion theorems.

This is an improved and shortened version of arXiv:1109.4646

References in corpus (1)

• On the generalized Zalcman functional for some classes of univalent functions

Cited by in corpus (3)

• Zalcman Conjecture for certain analytic and univalent functions
• Zalcman and generalized Zalcman conjecture for the class $\mathcal{U}$
• Generalized Zalcman conjecture for some classes of analytic functions