Conformal representation:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Cambridge
Cambridge University Press
1969
|
| Ausgabe: | Second edition, reprinted |
| Schriftenreihe: | Cambridge Tracts in Mathematics and Mathematical Physics
28 |
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | IX, 115 Seiten Illustrationen |
Internformat
MARC
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| 245 | 1 | 0 | |a Conformal representation |c by C. Carathéodory |
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| 300 | |a IX, 115 Seiten |b Illustrationen | ||
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Datensatz im Suchindex
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| adam_text | CONTENTS
PAGE
PREFACE v
INTRODUCTION. Historical Summary 1
CHAP.
I. MOBIUS TRANSFORMATION
§ 5. Conformal representation in general .... 3
§§ 6-9. Mobius Transformation 4
§§ 10-12. Invariance of the cross-ratio 5
§§13-15. Pencils of circles 7
§§ 16-22. Bundles of circles 8
§§ 23-25. Inversion with respect to a circle ... 11
§§ 26-30. Geometry of Mobius Transformations ... 13
II. NON-EUCLIDEAN GEOMETRY
§§ 31-34. Inversion with respect to the circles of a bundle . 16
§ 35. Representation of a circular area on itself . . . 17
§§ 36, 37. Non-Euclidean Geometry 18
§§ 38-41. Angle and distance 19
§ 42. The triangle theorem 21
§ 43. Non-Euclidean length of a curve 22
§ 44. Geodesic curvature 22
§§ 45-47. Non-Euclidean motions 23
§ 48. Parallel curves 25
III. ELEMENTARY TRANSFORMATIONS
§§ 49-51. The exponential function 26
§§ 52, 53. Representation of a rectilinear strip on a circle . 27
§ 54. Representation of a circular crescent .... 28
§§ 55-59. Representation of Riemann surfaces ... 29
§§ 60, 61. Representation of the exterior of an ellipse . . 31
§§ 62-66. Representation of an arbitrary simply-connected
domain on a bounded domain 32
IV. SCHWARZ S LEMMA
§ 67. Schwarz s Theorem 39
§ 68. Theorem of uniqueness for the conformal representation
of simply-connected domains ...... 40
§ 69. Liouville s Theorem 40
§§ 70-73. Invariant enunciation of Schwarz s Lemma . . 41
§ 74. Functions with positive real parts .... 43
§ 75. Harnack s Theorem 44
§ 76. Functions with bounded real parts .... 45
§§ 77-79. Surfaces with algebraic and logarithmic branch¬
points 45
viii CONTENTS
CHAP. PAGE
IV. §§ ii 0~82. Representation of simple domains .... 46
§§ 83 - 35. Representation upon one another of domains con¬
taining circular areas 50
§ 86. . ..Problem 52
|| 87, 6*8. Extensions of Schwarz s Lemma .... 52
§§ 89-9S . Julia s Theorem 53
V. THE FUNDAMENTAL THEOREMS OF CONFORMAL
REPRESENTATION
§ 94. Continuous convergence 58
§§ 95,, 96. Limiting oscillation 58
§§ 97-99. Normal families of bounded functions . . . 61
§ 100. Existence of the solution in certain problems of the
calculus of variations 62
§§ 101-103. Normal families of regular analytic functions . 63
§ 104. Application to conformal representation ... 66
§§105-118. The maim theorem of conformal representation . 66
§ 119. Normal families composed of functions which trans¬
form simple domains into circles 73
§§120-123. The kernel of a sequence of domains . . . 74
§ 124. Examples 77
§§ 125-130. Simultaneous conformal transformation of do¬
mains lying each within another 77
VI. TRANSFORMATION OF THE FRONTIER
§§131-133. An inequality due to Lindelof .... 81
§§ 134, 135. Lemma 1, on representation of the frontier . 82
§ 136. Lemma 2 84
§§ 137, 138. Transformation of one Jordan domain into
another . 85
§§ 139, 140. Inversion with respect to an analytic curve . 87
§§ 141-145. The inversion principle 88
§§ 146-151. Transformation of corners 91
§§ 152, 153. Confonn.al transformation on the frontier . . 96
VII. TRANSFORMATION OF CLOSED SURFACES
§§ 154, 155. Blending of domains 98
§ 156. Conformal transformation of a three-dimensional sur¬
face 99
§§ 157-161. Conformal representation of a closed surface on
a sphere 100
CONTENTS ix
CHAP. PAQK
VIII. THE GENERAL THEOREM OF UNIFORM1SATION
§§ 162, 163, 164. Abstract surfaces 103
jj{$ 165, 166. The universal covering surface .... 104
§ 167. Domains and their boundaries 105
§ 168. The Theorem of van der Waerden .... 106
S1C9. Riemann surfaces 108
§§170,171. The Uniformisation Theorem . . . .110
§172. Oonformal representation of a torus . . . .111
BIBLIOGRAPHICAL NOTES 113
|
| any_adam_object | 1 |
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| illustrated | Illustrated |
| indexdate | 2024-07-09T15:37:31Z |
| institution | BVB |
| language | English |
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| owner_facet | DE-91G DE-BY-TUM DE-355 DE-BY-UBR DE-188 |
| physical | IX, 115 Seiten Illustrationen |
| publishDate | 1969 |
| publishDateSearch | 1969 |
| publishDateSort | 1969 |
| publisher | Cambridge University Press |
| record_format | marc |
| series | Cambridge Tracts in Mathematics and Mathematical Physics |
| series2 | Cambridge Tracts in Mathematics and Mathematical Physics |
| spelling | Carathéodory, Constantin 1873-1950 Verfasser (DE-588)118667076 aut Conformal representation by C. Carathéodory Second edition, reprinted Cambridge Cambridge University Press 1969 IX, 115 Seiten Illustrationen txt rdacontent n rdamedia nc rdacarrier Cambridge Tracts in Mathematics and Mathematical Physics 28 Functions Geometry, Non-Euclidean Surfaces, Representation of Konforme Abbildung (DE-588)4164968-0 gnd rswk-swf Konforme Abbildung (DE-588)4164968-0 s DE-604 Cambridge Tracts in Mathematics and Mathematical Physics 28 (DE-604)BV001887938 28 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=001261654&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Carathéodory, Constantin 1873-1950 Conformal representation Cambridge Tracts in Mathematics and Mathematical Physics Functions Geometry, Non-Euclidean Surfaces, Representation of Konforme Abbildung (DE-588)4164968-0 gnd |
| subject_GND | (DE-588)4164968-0 |
| title | Conformal representation |
| title_auth | Conformal representation |
| title_exact_search | Conformal representation |
| title_full | Conformal representation by C. Carathéodory |
| title_fullStr | Conformal representation by C. Carathéodory |
| title_full_unstemmed | Conformal representation by C. Carathéodory |
| title_short | Conformal representation |
| title_sort | conformal representation |
| topic | Functions Geometry, Non-Euclidean Surfaces, Representation of Konforme Abbildung (DE-588)4164968-0 gnd |
| topic_facet | Functions Geometry, Non-Euclidean Surfaces, Representation of Konforme Abbildung |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=001261654&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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