Polygonal quasiconformal maps and grunsky inequalities

2003 ◽  
Vol 90 (1) ◽  
pp. 175-196 ◽  
Author(s):  
Samuel L. Krushkal
Keyword(s):  
Quasiconformal Maps ◽  
Grunsky Inequalities

Teichmuller Geometry

2017 ◽  
Author(s):  
Benson Farb ◽  
Dan Margalit
Keyword(s):  
Uniqueness Theorem ◽  
Existence Theorems ◽  
Quadratic Differentials ◽  
Complex Structures ◽  
Metric Geometry ◽  
Quasiconformal Maps ◽  
Hyperbolic Structures ◽  
Teichmüller Metric ◽  
Uniqueness And Existence ◽  
Teichmüller Mapping

This chapter focuses on the metric geometry of Teichmüller space. It first explains how one can think of Teich(Sɡ) as the space of complex structures on Sɡ. To this end, the chapter defines quasiconformal maps between surfaces and presents a solution to the resulting Teichmüller's extremal problem. It also considers the correspondence between complex structures and hyperbolic structures, along with the Teichmüller mapping, Teichmüller metric, and the proof of Teichmüller's uniqueness and existence theorems. The fundamental connection between Teichmüller's theorems, holomorphic quadratic differentials, and measured foliations is discussed as well. Finally, the chapter describes the Grötzsch's problem, whose solution is tied to the proof of Teichmüller's uniqueness theorem.

Local boundary dilatation of quasiconformal maps

2005 ◽  
Vol 48 (6) ◽  
pp. 798
Author(s):  
Yi QI
Keyword(s):  
Quasiconformal Maps ◽  
Local Boundary

Singular values, quasiconformal maps and the Schottky upper bound

1998 ◽  
Vol 41 (12) ◽  
pp. 1241-1247 ◽  
Author(s):  
Songliang Qiu
Keyword(s):  
Upper Bound ◽  
Singular Values ◽  
Quasiconformal Maps

Maximal Functions, A ∞ -Measures, and Quasiconformal Maps

1991 ◽  
Vol 113 (3) ◽  
pp. 689
Author(s):  
Susan G. Staples
Keyword(s):  
Maximal Functions ◽  
Quasiconformal Maps

scholarly journals Quasiconformal maps of bordered Riemann surfaces with L 2 Beltrami differentials

2017 ◽  
Vol 132 (1) ◽  
pp. 229-245
Author(s):  
David Radnell ◽  
Eric Schippers ◽  
Wolfgang Staubach
Keyword(s):  
Riemann Surfaces ◽  
Quasiconformal Maps

scholarly journals Quasiconformal maps in metric spaces with controlled geometry

1998 ◽  
Vol 181 (1) ◽  
pp. 1-61 ◽  
Author(s):  
Juha Heinonen ◽  
Pekka Koskela
Keyword(s):  
Metric Spaces ◽  
Quasiconformal Maps

scholarly journals Quasiconformal maps in manifolds

1967 ◽  
Vol 1967 ◽  
pp. 1-39 ◽  
Author(s):  
Kalevi Suominen
Keyword(s):  
Quasiconformal Maps

String theory and quasiconformal maps

2017 ◽  
Vol 38 (2) ◽  
pp. 352-363 ◽  
Author(s):  
A. G. Sergeev
Keyword(s):  
String Theory ◽  
Quasiconformal Maps

Formulas for the Nehari Coefficients of Bounded Univalent Functions

1977 ◽  
Vol 29 (3) ◽  
pp. 587-605
Author(s):  
Duane W. De Temple ◽  
David B. Oulton
Keyword(s):  
Unit Disc ◽  
Univalent Functions ◽  
Bieberbach Conjecture ◽  
Grunsky Inequalities

The Grunsky inequalities [6] and their generalizations (e.g., [5; 14; 17]) have become an increasingly important tool for the study of the coefficients of normalized univalent functions defined on the unit disc. In particular, proofs based upon the Grunsky inequalities have now settled the Bieberbach conjecture for the fifth [15] and sixth [13] coefficients. For bounded univalent functions the situation is similar, although the Grunsky inequalities go over to those of Nehari [11].

scholarly journals Computing Extremal Quasiconformal Maps

2012 ◽  
Vol 31 (5) ◽  
pp. 1679-1689 ◽  
Author(s):  
Ofir Weber ◽  
Ashish Myles ◽  
Denis Zorin
Keyword(s):  
Quasiconformal Maps
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