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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