Lectures on minimal surfaces: 1 Introduction, fundamentals, geometry and basic boundary value problems
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| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Cambridge [u.a.]
Cambridge Univ. Press
1989
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| Online Access: | Inhaltsverzeichnis |
| Item Description: | Literaturverz. S. 489 - 546 |
| Physical Description: | XXV, 563 S. Ill., graph. Darst. |
| ISBN: | 0521244277 |
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| 240 | 1 | 0 | |a Vorlesungen über Minimalflächen |
| 245 | 1 | 0 | |a Lectures on minimal surfaces |n 1 |p Introduction, fundamentals, geometry and basic boundary value problems |c Johannes C. C. Nitsche |
| 264 | 1 | |a Cambridge [u.a.] |b Cambridge Univ. Press |c 1989 | |
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Record in the Search Index
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|---|---|
| adam_text | CONTENTS
Preface to the English edition vii
Preface to the German edition xix
I Introduction 1
II Curves and surfaces 27
1 Curves 27
2 Surfaces 38
3 Differential geometric surfaces 50
4 Minimal surfaces 61
5 Special minimal surfaces I 68
5.1 Catenoid, helicoids, Scherk s surface 68
5.2 Minimal surfaces of the form f(x) { g(y) + h(z) = 0 71
5.3 Enneper s minimal surface 80
5.4 Cyclic minimal surfaces 85
6 The second variation of surface area 90
III Conformal mapping of minimal surfaces 117
1 Conformal mapping of open, nonparametric surfaces 117
1.1 Local conformal mapping. Properties of solutions to the minimal
surface equation 117
1.2 Global conformal mapping 126
1.3 Lemmas from complex analysis 129
1.4 The asymptotic behavior of solutions to the minimal surface equation 135
2 Conformal mapping of open, parametric minimal surfaces 137
2.1 General theorems 137
2.2 Special minimal surfaces II. Catalan s, Enneper s, and Henneberg s
surfaces 140
2.3 The Weierstrass Enneper representation formulas 145
2.4 Special minimal surfaces III. Generalized Scherk surfaces 151
xxiv Contents
2.5 Algebraic minimal surfaces 159
2.6 Special minimal surfaces IV. Minimal surfaces with plane lines
of curvature 162
2.7 Associate minimal surfaces 166
3 Conformal mapping of minimal surfaces bounded by Jordan curves 169
IV Results from analysis 176
1 Functions of class 3JI 177
2 Surfaces of class 2R 195
3 Properties of harmonic functions 198
4 Mappings with bounded Dirichlet integrals 202
5 The topological index of a plane closed curve 210
6 The linear measure of point sets in the plane 215
7 Point sets of vanishing logarithmic capacity 228
V Plateau s problem 233
1 The solution of Plateau s problem 233
1.1 Special minimal surfaces V. The Riemann Schwarz minimal surface 233
1.2 Historical preface 242
1.3 The existence proof. First properties of the solutions 252
1.4 The method of descent 267
1.5 The functionals of Douglas and Shiffman 269
2 Properties of the solution to Plateau s problem 272
2.1 The boundary behavior 272
2.2 Branch points 314
2.3 Uniqueness and nonuniqueness 338
3 The nonparametric problem 352
4 The existence of unstable minimal surfaces 373
4.1 Preliminary remarks 373
4.2 The existence proof 380
4.3 Examples 391
5 The problem of least area 393
5.1 Minimal surfaces with common points 393
5.2 Concerning the absolute minimum of surface area 399
6 The structure of surfaces of smallest area 407
6.1 Almost conformal mappings 407
6.2 Concerning the regularity for surfaces of smallest area 411
Appendix A 423
Al Local behavior of solutions to elliptic differential inequalities 423
A2 Concerning the Bernstein problem 429
A3 Uniqueness for Enneper s minimal surface 436
A4 On the question of finiteness for Plateau s problem 439
A5 Stable minimal surfaces 448
Contents xxv
A6 The theorem of F. Xavier 457
A7 Open problems 460
A8 Coda additions in proof 465
References 489
Name index 547
Subject index 555
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| any_adam_object | 1 |
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| author_sort | Nitsche, Johannes C. C. 1925-2006 |
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| building | Verbundindex |
| bvnumber | BV003714058 |
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| id | DE-604.BV003714058 |
| illustrated | Illustrated |
| indexdate | 2024-07-09T16:04:16Z |
| institution | BVB |
| isbn | 0521244277 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-002364087 |
| oclc_num | 311089572 |
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| physical | XXV, 563 S. Ill., graph. Darst. |
| publishDate | 1989 |
| publishDateSearch | 1989 |
| publishDateSort | 1989 |
| publisher | Cambridge Univ. Press |
| record_format | marc |
| spelling | Nitsche, Johannes C. C. 1925-2006 Verfasser (DE-588)10839896X aut Vorlesungen über Minimalflächen Lectures on minimal surfaces 1 Introduction, fundamentals, geometry and basic boundary value problems Johannes C. C. Nitsche Cambridge [u.a.] Cambridge Univ. Press 1989 XXV, 563 S. Ill., graph. Darst. txt rdacontent n rdamedia nc rdacarrier Literaturverz. S. 489 - 546 (DE-604)BV003714057 1 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=002364087&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Nitsche, Johannes C. C. 1925-2006 Lectures on minimal surfaces |
| title | Lectures on minimal surfaces |
| title_alt | Vorlesungen über Minimalflächen |
| title_auth | Lectures on minimal surfaces |
| title_exact_search | Lectures on minimal surfaces |
| title_full | Lectures on minimal surfaces 1 Introduction, fundamentals, geometry and basic boundary value problems Johannes C. C. Nitsche |
| title_fullStr | Lectures on minimal surfaces 1 Introduction, fundamentals, geometry and basic boundary value problems Johannes C. C. Nitsche |
| title_full_unstemmed | Lectures on minimal surfaces 1 Introduction, fundamentals, geometry and basic boundary value problems Johannes C. C. Nitsche |
| title_short | Lectures on minimal surfaces |
| title_sort | lectures on minimal surfaces introduction fundamentals geometry and basic boundary value problems |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=002364087&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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