E-Book, Englisch, 156 Seiten
Reihe: Frontiers in Mathematics
Avkhadiev / Wirths Schwarz-Pick Type Inequalities
1. Auflage 2009
ISBN: 978-3-0346-0000-2
Verlag: Springer
Format: PDF
Kopierschutz: 1 - PDF Watermark
E-Book, Englisch, 156 Seiten
Reihe: Frontiers in Mathematics
ISBN: 978-3-0346-0000-2
Verlag: Springer
Format: PDF
Kopierschutz: 1 - PDF Watermark
This book gives a unified representation of generalizations of the Schwarz Lemma. It examines key coefficient theorems of the last century and explains the connection between coefficient estimates and characteristics of the hyperbolic geometry in a domain.
Autoren/Hrsg.
Weitere Infos & Material
1;Contents;7
2;Introduction;9
2.1;1.1 Historical remarks;9
2.2;1.2 On inequalities for higher derivatives;11
2.3;1.3 On methods;13
2.4;1.4 Survey of the contents;14
3;Basic coefficient inequalities;15
3.1;2.1 Subordinate functions;15
3.2;2.2 Bieberbach’s conjecture by de Branges;19
3.3;2.3 Theorems of Jenkins and Sheil-Small;23
3.4;2.4 Inverse coefficients;26
3.5;2.5 Domains with bounded boundary rotation;31
4;The Poincar´e metric;35
4.1;3.1 Background;35
4.2;3.2 The Schwarz-Pick inequality;38
4.3;3.3 Estimates using the Euclidean distance;41
4.4;3.4 An application of Teichmüller’s theorem;45
4.5;3.5 Domains with uniformly perfect boundary;48
4.6;3.6 Derivatives of the conformal radius;52
5;Basic Schwarz-Pick type inequalities;57
5.1;4.1 Two classical inequalities;58
5.2;4.2 Theorems of Ruscheweyh and Yamashita;60
5.3;4.3 Pairs of simply connected domains;63
5.4;4.4 Holomorphic mappings into convex domains;67
5.5;4.5 Punishing factors for convex pairs;71
5.6;4.6 Case n = 2 for all domains;74
6;Punishing factors for special cases;77
6.1;5.1 Solution of the Chua conjecture;77
6.2;5.2 Punishing factors for angles;80
6.3;5.3 Sharp lower bounds for punishing factors;86
6.4;5.4 Domains in the extended complex plane;92
6.5;5.5 Maps from convex into concave domains;98
7;Multiply connected domains;104
7.1;6.1 Finitely connected domains;104
7.2;6.2 Pairs of arbitrary domains;111
7.3;6.3 Some examples;115
8;Related results;120
8.1;7.1 Inequalities for schlicht functions;120
8.2;7.2 Derivatives of a-invariant functions;124
8.3;7.3 A characterization of convex domains;131
9;Some open problems;134
9.1;8.1 The Krzyz conjecture;134
9.2;8.2 The angle conjecture;135
9.3;8.3 The generalized Goodman conjecture;138
9.4;8.4 Bloch and several variable problems;146
9.5;8.5 On sums of inverse coefficients;147
10;Bibliography;150
11;Index;161
