Regularity of minimal surfaces:
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| Main Authors: | , , |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Heidelberg u. a.
Springer
2010
|
| Edition: | Rev. and enl. 2. ed. |
| Series: | Grundlehren der mathematischen Wissenschaften
340 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | XVII, 623 S. Ill., graph. Darst. |
| ISBN: | 9783642116995 9783642117008 |
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MARC
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| 245 | 1 | 0 | |a Regularity of minimal surfaces |c Ulrich Dierkes, Stefan Hildebrandt, Anthony J. Tromba |
| 250 | |a Rev. and enl. 2. ed. | ||
| 264 | 1 | |a Heidelberg u. a. |b Springer |c 2010 | |
| 300 | |a XVII, 623 S. |b Ill., graph. Darst. | ||
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Record in the Search Index
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| adam_text | IMAGE 1
CONTENTS
PART I. BOUNDARY BEHAVIOUR OF MINIMAL SURFACES
CHAPTER 1. MINIMAL SURFACES WITH FREE BOUNDARIES 3
1.1 SURFACES OF CLASS H AND HOMOTOPY CLASSES OF THEIR BOUNDARY CURVES.
NONSOLVABILITY OF THE FREE BOUNDARY PROBLEM WITH FIXED HOMOTOPY TYPE OF
THE BOUNDARY TRACES 5
1.2 CLASSES OF ADMISSIBLE FUNCTIONS. LINKING CONDITION 18 1.3 EXISTENCE
OF MINIMIZERS FOR THE FREE BOUNDARY PROBLEM . . .. 21 1.4 STATIONARY
MINIMAL SURFACES WITH FREE OR PARTIALLY FREE BOUNDARIES AND THE
TRANSVERSALITY CONDITION 28
1.5 NECESSARY CONDITIONS FOR STATIONARY MINIMAL SURFACES 35 1.6
EXISTENCE OF STATIONARY MINIMAL SURFACES IN A SIMPLEX 39 1.7 STATIONARY
MINIMAL SURFACES OF DISK-TYPE IN A SPHERE 41
1.8 REPORT ON THE EXISTENCE OF STATIONARY MINIMAL SURFACES IN CONVEX
BODIES 43
1.9 NONUNIQUENESS OF SOLUTIONS TO A FREE BOUNDARY PROBLEM. FAMILIES OF
SOLUTIONS 45
1.10 SCHOLIA 65
CHAPTER 2. THE BOUNDARY BEHAVIOUR OF MINIMAL SURFACES 75
2.1 POTENTIAL-THEORETIC PREPARATIONS 76
2.2 SOLUTIONS OF DIFFERENTIAL INEQUALITIES 90
2.3 THE BOUNDARY REGULARITY OF MINIMAL SURFACES BOUNDED BY JORDAN ARCS
102
2.4 THE BOUNDARY BEHAVIOUR OF MINIMAL SURFACES AT THEIR FREE BOUNDARY: A
SURVEY OF THE RESULTS AND AN OUTLINE OF THEIR PROOFS 112
BIBLIOGRAFISCHE INFORMATIONEN HTTP://D-NB.INFO/1007428600
DIGITALISIERT DURCH
IMAGE 2
VIII CONTENTS
2.5 HOLDER CONTINUITY FOR MINIMA 118
2.6 HOLDER CONTINUITY FOR STATIONARY SURFACES 130
2.7 C^^-REGULARITY 153
2.8 HIGHER REGULARITY IN CASE OF SUPPORT SURFACES WITH EMPTY BOUNDARIES.
ANALYTIC CONTINUATION ACROSS A FREE BOUNDARY 174
2.9 A DIFFERENT APPROACH TO BOUNDARY REGULARITY 181 2.10 ASYMPTOTIC
EXPANSION OF MINIMAL SURFACES AT BOUNDARY BRANCH POINTS AND GEOMETRIC
CONSEQUENCES 189 2.11 THE GAUSS-BONNET FORMULA FOR BRANCHED MINIMAL
SURFACES . 193 2.12 SCHOLIA 200
CHAPTER 3. SINGULAR BOUNDARY POINTS OF MINIMAL SURFACES 213
3.1 THE METHOD OF HARTMAN AND WINTNER, AND ASYMPTOTIC EXPANSIONS AT
BOUNDARY BRANCH POINTS 214
3.2 A GRADIENT ESTIMATE AT SINGULARITIES CORRESPONDING TO CORNERS OF THE
BOUNDARY 235
3.3 MINIMAL SURFACES WITH PIECEWISE SMOOTH BOUNDARY CURVES AND THEIR
ASYMPTOTIC BEHAVIOUR AT CORNERS 245
3.4 AN ASYMPTOTIC EXPANSION FOR SOLUTIONS OF THE PARTIALLY FREE BOUNDARY
PROBLEM 259
3.5 SCHOLIA 271
3.5.1 REFERENCES 271
3.5.2 HOLDER CONTINUITY AT INTERSECTION POINTS 271
PART II. GEOMETRIC PROPERTIES OF MINIMAL SURFACES AND JF-SURFACES
CHAPTER 4. ENCLOSURE AND EXISTENCE THEOREMS FOR MINIMAL SURFACES AND
//-SURFACES. ISOPERIMETRIC INEQUALITIES 279
4.1 APPLICATIONS OF THE MAXIMUM PRINCIPLE AND NONEXISTENCE OF MULTIPLY
CONNECTED MINIMAL SURFACES WITH PRESCRIBED BOUNDARIES 280
4.2 TOUCHING IF-SURFACES AND ENCLOSURE THEOREMS. FURTHER NONEXISTENCE
RESULTS 284
4.3 MINIMAL SUBMANIFOLDS AND SUBMANIFOLDS OF BOUNDED MEAN CURVATURE. AN
OPTIMAL NONEXISTENCE RESULT 295 4.3.1 AN OPTIMAL NONEXISTENCE RESULT FOR
MINIMAL SUBMANIFOLDS OF CODIMENSION ONE 311
4.4 GEOMETRIC MAXIMUM PRINCIPLES 314
4.4.1 THE BARRIER PRINCIPLE FOR SUBMANIFOLDS OF ARBITRARY CODIMENSION
314
4.4.2 A GEOMETRIC INCLUSION PRINCIPLE FOR STRONG SUBSOLUTIONS 322
IMAGE 3
CONTENTS IX
4.5 ISOPERIMETRIC INEQUALITIES 332
4.6 ESTIMATES FOR THE LENGTH OF THE FREE TRACE 346
4.7 OBSTACLE PROBLEMS AND EXISTENCE RESULTS FOR SURFACES OF PRESCRIBED
MEAN CURVATURE 371
4.8 SURFACES OF PRESCRIBED MEAN CURVATURE IN A RIEMANNIAN MANIFOLD 407
4.8.1 ESTIMATES FOR JACOBI FIELDS 408
4.8.2 RIEMANN NORMAL COORDINATES 418
4.8.3 SURFACES OF PRESCRIBED MEAN CURVATURE IN A RIEMANNIAN MANIFOLD 424
4.9 SCHOLIA 431
4.9.1 ENCLOSURE THEOREMS AND NONEXISTENCE 431
4.9.2 THE ISOPERIMETRIC PROBLEM. HISTORICAL REMARKS AND REFERENCES TO
THE LITERATURE 433
4.9.3 EXPERIMENTAL PROOF OF THE ISOPERIMETRIC INEQUALITY . .. 435 4.9.4
ESTIMATES FOR THE LENGTH OF THE FREE TRACE 435
4.9.5 THE PLATEAU PROBLEM FOR H-SURFACES 437
CHAPTER 5. THE THREAD PROBLEM 441
5.1 EXPERIMENTS AND EXAMPLES. MATHEMATICAL FORMULATION OF THE SIMPLEST
THREAD PROBLEM 441
5.2 EXISTENCE OF SOLUTIONS TO THE THREAD PROBLEM 446
5.3 ANALYTICITY OF THE MOVABLE BOUNDARY 463
5.4 SCHOLIA 483
CHAPTER 6. BRANCH POINTS 487
6.1 THE FIRST FIVE VARIATIONS OF DIRICHLET S INTEGRAL, AND FORCED JACOBI
FIELDS 488
6.2 THE THEOREM FOR N + 1 EVEN AND M + 1 ODD 519
6.3 BOUNDARY BRANCH POINTS 528
6.4 SCHOLIA 554
BIBLIOGRAPHY 561
INDEX 619
|
| any_adam_object | 1 |
| author | Dierkes, Ulrich 1956- Hildebrandt, Stefan 1936-2015 Tromba, Anthony J. 1943- |
| author_GND | (DE-588)142533912 (DE-588)119219050 (DE-588)142684996 |
| author_facet | Dierkes, Ulrich 1956- Hildebrandt, Stefan 1936-2015 Tromba, Anthony J. 1943- |
| author_role | aut aut aut |
| author_sort | Dierkes, Ulrich 1956- |
| author_variant | u d ud s h sh a j t aj ajt |
| building | Verbundindex |
| bvnumber | BV036859195 |
| classification_rvk | SK 370 |
| ctrlnum | (OCoLC)670417685 (DE-599)BVBBV036859195 |
| dewey-full | 516.362 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 516 - Geometry |
| dewey-raw | 516.362 |
| dewey-search | 516.362 |
| dewey-sort | 3516.362 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| edition | Rev. and enl. 2. ed. |
| format | Book |
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| id | DE-604.BV036859195 |
| illustrated | Illustrated |
| indexdate | 2024-07-09T22:49:34Z |
| institution | BVB |
| isbn | 9783642116995 9783642117008 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-020774999 |
| oclc_num | 670417685 |
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| owner | DE-384 |
| owner_facet | DE-384 |
| physical | XVII, 623 S. Ill., graph. Darst. |
| publishDate | 2010 |
| publishDateSearch | 2010 |
| publishDateSort | 2010 |
| publisher | Springer |
| record_format | marc |
| series | Grundlehren der mathematischen Wissenschaften |
| series2 | Grundlehren der mathematischen Wissenschaften |
| spelling | Dierkes, Ulrich 1956- Verfasser (DE-588)142533912 aut Regularity of minimal surfaces Ulrich Dierkes, Stefan Hildebrandt, Anthony J. Tromba Rev. and enl. 2. ed. Heidelberg u. a. Springer 2010 XVII, 623 S. Ill., graph. Darst. txt rdacontent n rdamedia nc rdacarrier Grundlehren der mathematischen Wissenschaften 340 Minimalfläche (DE-588)4127814-8 gnd rswk-swf Randregularität (DE-588)4667263-1 gnd rswk-swf Minimalfläche (DE-588)4127814-8 s Randregularität (DE-588)4667263-1 s DE-604 Hildebrandt, Stefan 1936-2015 Verfasser (DE-588)119219050 aut Tromba, Anthony J. 1943- Verfasser (DE-588)142684996 aut Grundlehren der mathematischen Wissenschaften 340 (DE-604)BV000000395 340 DNB Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=020774999&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Dierkes, Ulrich 1956- Hildebrandt, Stefan 1936-2015 Tromba, Anthony J. 1943- Regularity of minimal surfaces Grundlehren der mathematischen Wissenschaften Minimalfläche (DE-588)4127814-8 gnd Randregularität (DE-588)4667263-1 gnd |
| subject_GND | (DE-588)4127814-8 (DE-588)4667263-1 |
| title | Regularity of minimal surfaces |
| title_auth | Regularity of minimal surfaces |
| title_exact_search | Regularity of minimal surfaces |
| title_full | Regularity of minimal surfaces Ulrich Dierkes, Stefan Hildebrandt, Anthony J. Tromba |
| title_fullStr | Regularity of minimal surfaces Ulrich Dierkes, Stefan Hildebrandt, Anthony J. Tromba |
| title_full_unstemmed | Regularity of minimal surfaces Ulrich Dierkes, Stefan Hildebrandt, Anthony J. Tromba |
| title_short | Regularity of minimal surfaces |
| title_sort | regularity of minimal surfaces |
| topic | Minimalfläche (DE-588)4127814-8 gnd Randregularität (DE-588)4667263-1 gnd |
| topic_facet | Minimalfläche Randregularität |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=020774999&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV000000395 |
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