Inversion theory and conformal mapping / David E. Blair.

Format:

Book

Author/Creator:

Blair, David E., 1940-

Series:

Student mathematical library 1520-9121 ; v. 9.

Student mathematical library, 1520-9121 ; v. 9

Language:

English

Subjects (All):

Inversions (Geometry).

Conformal mapping.

Physical Description:

x, 118 pages : illustrations ; 22 cm.

Place of Publication:

Providence, RI : American Mathematical Society, 2000.

Contents:

Chapter 1. Classical Inversion Theory in the Piane 1

1.2. Cross ratio 9

1.3. Applications 14

1.4. Miquel's Theorem 17

1.5. Feuerbach's Theorem 21

Chapter 2. Linear Fractional Transformations 27

2.1. Complex numbers 27

2.2. The extended complex plane and stereographic projection 29

2.3. Linear fractional transformations 34

2.4. Cross ratio 37

2.5. Some special linear fractional transformations 39

2.6. Extended Mobius transformations 43

2.7. The Poincare models of hyperbolic geometry 52

2.8. A distortion theorem 59

Chapter 3. Advanced Calculus and Conformal Maps 63

3.1. Review of advanced calculus 63

3.2. Inner products 70

3.3. Conformal maps 73

Chapter 4. Conformal Maps in the Plane 75

4.1. Complex function theory 75

4.2. Abundance of conformal maps 78

Chapter 5. Conformal Maps in Euclidean Space 83

5.1. Inversion in spheres 83

5.2. Conformal maps in Euclidean space 87

5.3. Sphere preserving transformations 92

Chapter 6. The Classical Proof of Liouville's Theorem 95

6.1. Surface theory 95

6.2. The classical proof 103

Chapter 7. When Does Inversion Preserve Convexity? 107

7.1. Curve theory and convexity 107

7.2. Inversion and convexity 110

7.3. The problem for convex bodies 114.

Notes:

Includes bibliographical references (pages 115-116) and index.

ISBN:

0821826360

OCLC:

44084034