A Riemannian Bieberbach estimate
| dc.creator | Fontenele, Francisco | |
| dc.creator | Xavier, Frederico | |
| dc.date | 2009-05-15 | |
| dc.date.accessioned | 2026-07-07T13:15:40Z | |
| dc.date.available | 2026-07-07T13:15:40Z | |
| dc.description | 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 $f : D\to \Bbb R^n, n\geq 2$. 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. | |
| dc.identifier | https://arxiv.org/abs/0905.2604 | |
| dc.identifier | http://arxiv.org/abs/0905.2604 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/230544 | |
| dc.subject | Differential Geometry | |
| dc.subject | Complex Variables | |
| dc.subject | 30C50; 53A10 | |
| dc.title | A Riemannian Bieberbach estimate | |
| dc.type | text |