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Conformal representation:

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Bibliographische Detailangaben
Beteilige Person:	Carathéodory, Constantin 1873-1950 (VerfasserIn)
Format:	Buch
Sprache:	Englisch
Veröffentlicht:	Cambridge Cambridge University Press 1969
Ausgabe:	Second edition, reprinted
Schriftenreihe:	Cambridge Tracts in Mathematics and Mathematical Physics 28
Schlagwörter:	Functions Geometry, Non-Euclidean Surfaces, Representation of Konforme Abbildung
Links:	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
Umfang:	IX, 115 Seiten 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
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physical	IX, 115 Seiten Illustrationen
publishDate	1969
publishDateSearch	1969
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publisher	Cambridge University Press
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series	Cambridge Tracts in Mathematics and Mathematical Physics
series2	Cambridge Tracts in Mathematics and Mathematical Physics
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
volume_link	(DE-604)BV001887938
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