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- W1853242783 abstract "The Bieberbach estimate, a pivotal result in the classical theory of univalent functions, states that any injective holomorphic function $f$ on the open unit disc $D$ satisfies $|f(0)|leq 4 |f'(0)|$. We generalize the Bieberbach estimate by proving a version of the inequality that applies to all injective smooth conformal immersions $f : Dto Bbb R^n, ngeq 2$. The new estimate involves two correction terms. The first one is geometric, coming from the second fundamental form of the image surface $f(D)$. The second term is of a dynamical nature, and involves certain Riemannian quantities associated to conformal attractors. Our results are partly motivated by a conjecture in the theory of embedded minimal surfaces." @default.
- W1853242783 created "2016-06-24" @default.
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- W1853242783 date "2009-05-15" @default.
- W1853242783 modified "2023-09-27" @default.
- W1853242783 title "A Riemannian Bieberbach estimate" @default.
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