Harmonic Maps Between Surfaces (with a Special Chapter on Conformal Mappings) [1 ed.] 9780387133393, 0-387-13339-9
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English Pages 140 [142] Year 1984
Table of contents :
Introduction....Pages 1-12
Geometric considerations....Pages 12-18
Conformal mappings....Pages 18-38
Existence theorems for harmonic maps between surfaces....Pages 38-53
Uniqueness theorems....Pages 54-65
A-priori C 1,α -estimates....Pages 65-77
A-priori estimates from below for the functional determinant of harmonic diffeomorphisms....Pages 77-86
The existence of harmonic diffeomorphisms which solve a Dirichlet problem....Pages 86-90
C 1, α - a priori estimates for arbitrary domains. Non-variational existence proofs....Pages 90-98
Harmonic coordinates. C 2, α - a - priori estimates for harmonic maps....Pages 98-105
The existence of harmonic diffeomorphisms between surfaces....Pages 106-112
Applications of harmonic maps between surfaces....Pages 112-126
Introduction....Pages 1-12
Geometric considerations....Pages 12-18
Conformal mappings....Pages 18-38
Existence theorems for harmonic maps between surfaces....Pages 38-53
Uniqueness theorems....Pages 54-65
A-priori C 1,α -estimates....Pages 65-77
A-priori estimates from below for the functional determinant of harmonic diffeomorphisms....Pages 77-86
The existence of harmonic diffeomorphisms which solve a Dirichlet problem....Pages 86-90
C 1, α - a priori estimates for arbitrary domains. Non-variational existence proofs....Pages 90-98
Harmonic coordinates. C 2, α - a - priori estimates for harmonic maps....Pages 98-105
The existence of harmonic diffeomorphisms between surfaces....Pages 106-112
Applications of harmonic maps between surfaces....Pages 112-126
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