Conformal mapping: lectures given at Oklahoma A. and M. College, Dept. of Mathematics, summer session, 1951

Front Cover
Transcribed by Robert Osserman - Mathematics - 256 pages
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Contents

HARMONIC FUNCTIONS 1 Definition
8
Harnacks Principle
10
Schwartz Theorem
11
Symmetry Principle
12
Dirichlets Principle lh 7 Subharmonic Functions
15
Perrons Method
16
Barrier Functions
18
Regions regular for the Dirichlet Problem
20
Extremal properties of p z and qz
43
Slit mappings for arbitrary Q hi 8 Minimal slit regions
51
An extremal property of pq
54
Null sets of class D
56
An extremal property of p+q
60
Other canonical mappings
64
EXTREMAL METRIC 1 Statement of the problem
67
Explicit calculation of in some simple cases
71

Greens Function
23
C0NF0RMAL MAPPING 1 The Riemann Mapping Theorem
29
Multiply Connected Regions and Approximating Regions32
32
Topological Structure of Qn Differentials
33
U The Greens function and the generalized Greens Function
36
Slit mappings of Qn
38
U The comparison ani composition laws Ik 5 Historical note
78
Extremal distance
80
Proof that nE1E2 jy 8U 9 Further examples
88
Reduced extremal distance
92
Conclusion
96

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