Foreword 1
CHAPTER Ⅰ．PSEUDO-HARMONIC FUNCTIONS 1
1．Introduction 1
2．Pseudo-harmonic functions 5
3．Critical points of U on G 10
4．Critical points of U on (B) 11
5．Level arcs leading to a boundary point zo not an extremum point of U 14
6．Canonical neighborhoods of a boundary point zo not an extremum point of U 17
7．Multiple points 21
8．The sets Uc and their maximal boundary arcs w at the level c 25
9．The Euler characteristic Ec 26
10．Obtaining K＊c from Kc-e 28
11．The variation of Ec with increasing c 31
12．The principal theorem under boundary conditions A 34
13．Th case of constant boundary values 38
CHAPTER Ⅱ．DIFFERENTIABLE BOUNDARY VALUES 43
14．Boundary conditions A，B，C 43
15．Boundary conditions B 48
16．The vector index J of the boundary values 54
17．The vector index J as the degree of a map on a circle 58
CHAPTER Ⅲ．INTERIOR TRANSFORMATIONS 62
18．Locally simple curves 62
19．Interior transformations 65
20．First applications and extensions 69
CHAPTER Ⅳ．THE GENERAL ORDER THEOREM 79
21．An example 79
22．Locally simple boundary images 81
23．The existence of partial branch elements 84
24．The order，angular order theorem 90
25．Radó＇s theorem generalized 93
CHAPTER Ⅴ．DEFORMATIONS OF LOCALLY SIMPLE CURVES AND AND OF INTERIOR TRANSFORMATIONS 97
26．Objectives 97
27．The μ-length of curves 99
28．Admissible deformations of locally simple curves 107
29．Deformation classes of locally simple curves 116
30．The product of locally simple curves 120
31．The product of deformation classes 123
32．O-Deformations．Curves of order zero 127
33．O-Deformations．Curves of order q？0 130
34．Deformation classes of meromorphic functions and of interior transformations 136