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 -