Verfügbarkeit: Minimal surfaces

Minimal surfaces:

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Bibliographische Detailangaben
Hauptverfasser:	Dierkes, Ulrich 1956- (VerfasserIn), Hildebrandt, Stefan 1936-2015 (VerfasserIn), Sauvigny, Friedrich 1953- (VerfasserIn)
Format:	Buch
Sprache:	English
Veröffentlicht:	Heidelberg u. a. Springer 2010
Ausgabe:	Rev. and enl. 2. ed.
Schriftenreihe:	Grundlehren der mathematischen Wissenschaften 339
Schlagworte:	Plateau-Problem Randwertproblem Minimalfläche
Online-Zugang:	Inhaltsverzeichnis
Beschreibung:	XV, 688 S. Ill., graph. Darst.
ISBN:	9783642116988 9783642116971

Internformat

MARC


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Datensatz im Suchindex

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adam_text	IMAGE 1 CONTENTS PART I. INTRODUCTION TO THE GEOMETRY OF SURFACES AND TO MINIMAL SURFACES CHAPTER 1. DIFFERENTIAL GEOMETRY OF SURFACES IN THREE-DIMENSIONAL EUCLIDEAN SPACE 3 1.1 SURFACES IN EUCLIDEAN SPACE 4 1.2 GAUSS MAP, WEINGARTEN MAP. FIRST, SECOND AND THIRD FUNDAMENTAL FORM. MEAN CURVATURE AND GAUSS CURVATURE .. 9 1.3 GAUSS S REPRESENTATION FORMULA, CHRISTOFFEL SYMBOLS, GAUSS-CODAZZI EQUATIONS, THEOREMA EGREGIUM, MINDING S FORMULA FOR THE GEODESIC CURVATURE 24 1.4 CONFORMAI PARAMETERS, GAUSS-BONNET THEOREM 33 1.5 COVARIANT DIFFERENTIATION. THE BELTRAMI OPERATOR 39 1.6 SCHOLIA 47 CHAPTER 2. MINIMAL SURFACES 53 2.1 FIRST VARIATION OF AREA. MINIMAL SURFACES 54 2.2 NONPARAMETRIC MINIMAL SURFACES 58 2.3 CONFORMAI REPRESENTATION AND ANALYTICITY OF NONPARAMETRIC MINIMAL SURFACES 62 2.4 BERNSTEIN S THEOREM 66 2.5 TWO CHARACTERIZATIONS OF MINIMAL SURFACES 72 2.6 PARAMETRIC SURFACES IN CONFORMAI PARAMETERS. CONFORMAI REPRESENTATION OF MINIMAL SURFACES. GENERAL DEFINITION OF MINIMAL SURFACES 75 2.7 A FORMULA FOR THE MEAN CURVATURE 78 2.8 ABSOLUTE AND RELATIVE MINIMA OF AREA 82 2.9 SCHOLIA 86 BIBLIOGRAFISCHE INFORMATIONEN HTTP://D-NB.INFO/1007428619 DIGITALISIERT DURCH IMAGE 2 VIII CONTENTS CHAPTER 3. REPRESENTATION FORMULAS AND EXAMPLES OF MINIMAL SURFACES. 91 3.1 THE ADJOINT SURFACE. MINIMAL SURFACES AS ISOTROPIE CURVES IN C 3 . ASSOCIATE MINIMAL SURFACES 93 3.2 BEHAVIOR OF MINIMAL SURFACES NEAR BRANCH POINTS 104 3.3 REPRESENTATION FORMULAS FOR MINIMAL SURFACES . . . I LL 3.4 BJOERLING S PROBLEM. STRAIGHT LINES AND PLANAR LINES OF CURVATURE ON MINIMAL SURFACES. SCHWARZIAN CHAINS 124 3.5 EXAMPLES OF MINIMAL SURFACES 141 3.5.1 CATENOID AND HELICOID 141 3.5.2 SCHERK S SECOND SURFACE: THE GENERAL MINIMAL SURFACE OF HELICOIDAL TYPE 146 3.5.3 THE ENNEPER SURFACE 151 3.5.4 BOUR SURFACES 155 3.5.5 THOMSEN SURFACES 156 3.5.6 SCHERK S FIRST SURFACE 156 3.5.7 THE HENNEBERG SURFACE 166 3.5.8 CATALAN S SURFACE 171 3.5.9 SCHWARZ S SURFACE 182 3.6 COMPLETE MINIMAL SURFACES 183 3.7 OMISSIONS OF THE GAUSS MAP OF COMPLETE MINIMAL SURFACES . 190 3.8 SCHOLIA 200 COLOR PLATES 229 PART II. PLATEAU S PROBLEM CHAPTER 4. THE PLATEAU PROBLEM AND THE PARTIALLY FREE BOUNDARY PROBLEM 239 4.1 AREA FUNCTIONAL VERSUS DIRICHLET INTEGRAL 246 4.2 RIGOROUS FORMULATION OF PLATEAU S PROBLEM AND OF THE MINIMIZATION PROCESS 251 4.3 EXISTENCE PROOF, PART I: SOLUTION OF THE VARIATIONAL PROBLEM. 255 4.4 THE COURANT-LEBESGUE LEMMA 260 4.5 EXISTENCE PROOF, PART II: CONFORMALITY OF MINIMIZERS OF THE DIRICHLET INTEGRAL 263 4.6 VARIANT OF THE EXISTENCE PROOF. THE PARTIALLY FREE BOUNDARY PROBLEM 275 4.7 BOUNDARY BEHAVIOR OF MINIMAL SURFACES WITH RECTIFIABLE BOUNDARIES 282 4.8 REFLECTION PRINCIPLES 289 4.9 UNIQUENESS AND NONUNIQUENESS QUESTIONS 292 4.10 ANOTHER SOLUTION OF PLATEAU S PROBLEM BY MINIMIZING AREA . 299 4.11 THE MAPPING THEOREMS OF RIEMANN AND LICHTENSTEIN 305 4.12 SOLUTION OF PLATEAU S PROBLEM FOR NONRECTIFIABLE BOUNDARIES . 314 IMAGE 3 CONTENTS IX 4.13 PLATEAU S PROBLEM FOR CARIAN FUNCTIONALS 320 4.14 ISOPERIMETRIC INEQUALITIES 327 4.15 SCHOLIA 335 CHAPTER 5. STABLE MINIMAL- AND II-SURFACES 365 5.1 IF-SURFACES AND THEIR NORMALS 367 5.2 BONNET S MAPPING AND BONNET S SURFACE 371 5.3 THE SECOND VARIATION OF F FOR IF-SURFACES AND THEIR STABILITY 376 5.4 ON -STABLE IMMERSIONS OF CONSTANT MEAN CURVATURE 382 5.5 CURVATURE ESTIMATES FOR STABLE AND IMMERSED CMC-SURFACES . 389 5.6 NITSCHE S UNIQUENESS THEOREM AND FIELD-IMMERSIONS 395 5.7 SOME FINITENESS RESULTS FOR PLATEAU S PROBLEM 407 5.8 SCHOLIA 420 CHAPTER 6. UNSTABLE MINIMAL SURFACES 425 6.1 COURANT S FUNCTION 0 426 6.2 COURANT S MOUNTAIN PASS LEMMA 438 6.3 UNSTABLE MINIMAL SURFACES IN A POLYGON 442 6.4 THE DOUGLAS FUNCTIONAL. CONVERGENCE THEOREMS FOR HARMONIC MAPPINGS 450 6.5 WHEN IS THE LIMES SUPERIOR OF A SEQUENCE OF PATHS AGAIN A PATH? 461 6.6 UNSTABLE MINIMAL SURFACES IN RECTIFIABLE BOUNDARIES 463 6.7 SCHOLIA 472 6.7.1 HISTORICAL REMARKS AND REFERENCES TO THE LITERATURE.. 472 6.7.2 THE THEOREM OF THE WALL FOR MINIMAL SURFACES IN TEXTBOOKS 473 6.7.3 SOURCES FOR THIS CHAPTER 474 6.7.4 MULTIPLY CONNECTED UNSTABLE MINIMAL SURFACES 474 6.7.5 QUASI-MINIMAL SURFACES 474 CHAPTER 7. GRAPHS WITH PRESCRIBED MEAN CURVATURE 493 7.1 //-SURFACES WITH A ONE-TO-ONE PROJECTION ONTO A PLANE, AND THE NONPARAMETRIC DIRICHLET PROBLEM 494 7.2 UNIQUE SOLVABILITY OF PLATEAU S PROBLEM FOR CONTOURS WITH A NONCONVEX PROJECTION ONTO A PLANE 508 7.3 MISCELLANEOUS ESTIMATES FOR NONPARAMETRIC II-SURFACES 516 7.4 SCHOLIA 529 CHAPTER 8. INTRODUCTION TO THE DOUGLAS PROBLEM 531 8.1 THE DOUGLAS PROBLEM. EXAMPLES AND MAIN RESULT 532 8.2 CONFORMALITY OF MINIMIZERS OF D IN {R) 538 IMAGE 4 X CONTENTS 8.3 COHESIVE SEQUENCES OF MAPPINGS 552 8.4 SOLUTION OF THE DOUGLAS PROBLEM 561 8.5 USEFUL MODIFICATIONS OF SURFACES 563 8.6 DOUGLAS CONDITION AND DOUGLAS PROBLEM 568 8.7 FURTHER DISCUSSION OF THE DOUGLAS CONDITION 578 8.8 EXAMPLES 581 8.9 SCHOLIA 584 PROBLEMS 587 APPENDIX 1. ON RELATIVE MINIMIZERS OF AREA AND ENERGY 589 APPENDIX 2. MINIMAL SURFACES IN HEISENBERG GROUPS 597 BIBLIOGRAPHY 599 INDEX 681
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author	Dierkes, Ulrich 1956- Hildebrandt, Stefan 1936-2015 Sauvigny, Friedrich 1953-
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series	Grundlehren der mathematischen Wissenschaften
series2	Grundlehren der mathematischen Wissenschaften
spelling	Dierkes, Ulrich 1956- Verfasser (DE-588)142533912 aut Minimal surfaces Ulrich Dierkes, Stefan Hildebrandt, Friedrich Sauvigny Rev. and enl. 2. ed. Heidelberg u. a. Springer 2010 XV, 688 S. Ill., graph. Darst. txt rdacontent n rdamedia nc rdacarrier Grundlehren der mathematischen Wissenschaften 339 Plateau-Problem (DE-588)4174854-2 gnd rswk-swf Randwertproblem (DE-588)4048395-2 gnd rswk-swf Minimalfläche (DE-588)4127814-8 gnd rswk-swf Minimalfläche (DE-588)4127814-8 s Plateau-Problem (DE-588)4174854-2 s Randwertproblem (DE-588)4048395-2 s DE-604 Hildebrandt, Stefan 1936-2015 Verfasser (DE-588)119219050 aut Sauvigny, Friedrich 1953- Verfasser (DE-588)110083334 aut Grundlehren der mathematischen Wissenschaften 339 (DE-604)BV000000395 339 DNB Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=020774917&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis
spellingShingle	Dierkes, Ulrich 1956- Hildebrandt, Stefan 1936-2015 Sauvigny, Friedrich 1953- Minimal surfaces Grundlehren der mathematischen Wissenschaften Plateau-Problem (DE-588)4174854-2 gnd Randwertproblem (DE-588)4048395-2 gnd Minimalfläche (DE-588)4127814-8 gnd
subject_GND	(DE-588)4174854-2 (DE-588)4048395-2 (DE-588)4127814-8
title	Minimal surfaces
title_auth	Minimal surfaces
title_exact_search	Minimal surfaces
title_full	Minimal surfaces Ulrich Dierkes, Stefan Hildebrandt, Friedrich Sauvigny
title_fullStr	Minimal surfaces Ulrich Dierkes, Stefan Hildebrandt, Friedrich Sauvigny
title_full_unstemmed	Minimal surfaces Ulrich Dierkes, Stefan Hildebrandt, Friedrich Sauvigny
title_short	Minimal surfaces
title_sort	minimal surfaces
topic	Plateau-Problem (DE-588)4174854-2 gnd Randwertproblem (DE-588)4048395-2 gnd Minimalfläche (DE-588)4127814-8 gnd
topic_facet	Plateau-Problem Randwertproblem Minimalfläche
url	http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=020774917&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA
volume_link	(DE-604)BV000000395
work_keys_str_mv	AT dierkesulrich minimalsurfaces AT hildebrandtstefan minimalsurfaces AT sauvignyfriedrich minimalsurfaces

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