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arXiv · 1109.4646

Hyperbolic metrics, homogeneous holomorphic functionals and Zalcman's conjecture

Samuel L. Krushkal
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Abstract

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.

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Samuel L. Krushkal. 2012-08-14. Hyperbolic metrics, homogeneous holomorphic functionals and Zalcman's conjecture. https://arxiv.org/abs/1109.4646

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