2011/09/21 by Samuel L. Krushkal, Krushkal, Samuel L.
Mathematics · #Analytic and geometric function theory #Complex Variables (math.CV) #FOS: Mathematics #Geometry and complex manifolds #Holomorphic and Operator Theory
paper · pdf · doi:10.48550/arxiv.1109.4646
openalex publication_date 2011/09/21 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We show, using the Kobayashi and Caratheodory metrics on special holomorphic disks in the universal Teichmuller space, that a wide class of holomorphic functionals on the space of univalent functions in the disk is maximized by the Koebe function or by its root transforms; their extremality is forced by hyperbolic features. As consequences, this implies the proofs of the famous Zalcman and Bieberbach conjectures.