Quasiconformal maps of bordered Riemann surfaces with L2 Beltrami differentials

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Quasiconformal maps of bordered Riemann surfaces with L2 Beltrami differentials. / Radnell, David; Schippers, Eric; Staubach, Wolfgang.

julkaisussa: JOURNAL D ANALYSE MATHEMATIQUE, Vuosikerta 132, Nro 1, 29.06.2017, s. 229-245.

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Radnell, David ; Schippers, Eric ; Staubach, Wolfgang. / Quasiconformal maps of bordered Riemann surfaces with L2 Beltrami differentials. Julkaisussa: JOURNAL D ANALYSE MATHEMATIQUE. 2017 ; Vuosikerta 132, Nro 1. Sivut 229-245.

Bibtex - Lataa

@article{44a564bf69d149b68465ff792090a507,
title = "Quasiconformal maps of bordered Riemann surfaces with L2 Beltrami differentials",
abstract = "Let Σ be a Riemann surface of genus g bordered by n curves homeomorphic to the circle S1. Consider quasiconformal maps f: Σ→Σ1 such that the restriction to each boundary curve is a Weil-Petersson class quasisymmetry. We show that any such f is homotopic to a quasiconformal map whose Beltrami differential is L2 with respect to the hyperbolic metric on Σ. The homotopy H(t, •): Σ → Σ1 is independent of t on the boundary curves; that is, H(t, p) = f(p) for all p ∈ ∂Σ.",
author = "David Radnell and Eric Schippers and Wolfgang Staubach",
year = "2017",
month = "6",
day = "29",
doi = "10.1007/s11854-017-0020-9",
language = "English",
volume = "132",
pages = "229--245",
journal = "JOURNAL D ANALYSE MATHEMATIQUE",
issn = "0021-7670",
publisher = "Springer New York",
number = "1",

}

RIS - Lataa

TY - JOUR

T1 - Quasiconformal maps of bordered Riemann surfaces with L2 Beltrami differentials

AU - Radnell, David

AU - Schippers, Eric

AU - Staubach, Wolfgang

PY - 2017/6/29

Y1 - 2017/6/29

N2 - Let Σ be a Riemann surface of genus g bordered by n curves homeomorphic to the circle S1. Consider quasiconformal maps f: Σ→Σ1 such that the restriction to each boundary curve is a Weil-Petersson class quasisymmetry. We show that any such f is homotopic to a quasiconformal map whose Beltrami differential is L2 with respect to the hyperbolic metric on Σ. The homotopy H(t, •): Σ → Σ1 is independent of t on the boundary curves; that is, H(t, p) = f(p) for all p ∈ ∂Σ.

AB - Let Σ be a Riemann surface of genus g bordered by n curves homeomorphic to the circle S1. Consider quasiconformal maps f: Σ→Σ1 such that the restriction to each boundary curve is a Weil-Petersson class quasisymmetry. We show that any such f is homotopic to a quasiconformal map whose Beltrami differential is L2 with respect to the hyperbolic metric on Σ. The homotopy H(t, •): Σ → Σ1 is independent of t on the boundary curves; that is, H(t, p) = f(p) for all p ∈ ∂Σ.

U2 - 10.1007/s11854-017-0020-9

DO - 10.1007/s11854-017-0020-9

M3 - Article

VL - 132

SP - 229

EP - 245

JO - JOURNAL D ANALYSE MATHEMATIQUE

JF - JOURNAL D ANALYSE MATHEMATIQUE

SN - 0021-7670

IS - 1

ER -

ID: 14489133