Minimal submanifolds and related topics:
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| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
New Jersey [u.a.]
World Scientific
2003
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| Series: | Nankai tracts in mathematics
8 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | VIII, 262 S. graph. Darst. |
| ISBN: | 9812386874 |
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Record in the Search Index
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| adam_text | NANKAI TRACTS IN MATHEMATICS - VOL. 8 MINIMAL SUBMANIFOLDS AND RELATED
TOPICS YUANLONG XIN FUDAN UNIVERSITY, CHINA WORLD SCIENTIFIC NEW JERSEY
* LONDON * SINGAPORE * SHANGHAI- HONGKONG -TAIPEI * BANGALORE CONTENTS
PREFACE VII CHAPTER I. INTRODUCTION 1 1.1 THE SECOND FUNDAMENTAL FORM 1
1.2 THE FIRST VARIATIONAL FORMULA 7 1.3 MINIMAL SUBMANIFOLDS IN
EUCLIDEAN SPACE 11 1.4 MINIMAL SUBMANIFOLDS IN THE SPHERE 15 1.5
EXAMPLES 18 1.6 RIGIDITY THEOREMS 24 1.7 EXERCISES 36 CHAPTER II.
BERNSTEIN S THEOREM AND ITS GENERALIZATIONS 39 2.1 GAUSS MAP 39 2.2 THE
WEIERSTRASS REPRESENTATION 45 2.3 THE VALUE DISTRIBUTION OF THE IMAGE
UNDER THE GAUSS MAP 56 2.4 EXERCISES 71 CHAPTER III. WEIERSTRASS TYPE
REPRESENTATIONS 73 3.1 THE REPRESENTATION FOR SURFACES OF PRESCRIBED
MEAN CURVATURE 73 3.2 THE REPRESENTATION FOR CMC-1 SURFACES IN H 3 78
3.2.1 THE MINKOWSKI MODEL FOR H 3 78 3.2.2 THE MATRIX MODEL FOR H 3 80
3.2.3 CMC-1 SURFACES IN M 3 82 3.2.4 HYPERBOLIC GAUSS MAPS 89 3.3
EXERCISES 96 CHAPTER IV. PLATEAU S PROBLEM AND DOUGLAS-RADO SOLUTION 97
4.1 MATHEMATICAL FORMULATION 97 4.2 THE DIRICHLET PRINCIPLE 102 4.3
PROOF OF THE MAIN THEOREM 105 VI CONTENTS CHAPTER V. MINIMAL
SUBMANIFOLDS OF HIGHER CODIMENSION 113 5.1- KAHLER GEOMETRY AND
WIRTINGER S INEQUALITY 113 5.2 SPECIAL LAGRANGIAN SUBMANIFOLDS 124 5.2.1
ALGEBRAIC PRELIMINARIES 124 5.2.2 SPECIAL LAGRANGIAN SUBMANIFOLDS 128
5.2.3 EXAMPLES 134 5.3 EXERCISES 142 CHAPTER VI. STABLE MINIMAL
HYPERSURFACES 143 6.1 THE SECOND VARIATIONAL FORMULA 144 6.2 STABLE
MINIMAL HYPERSURFACES AND APPLICATIONS 153 6.3 A CLASSIFICATION OF
CERTAIN STABLE MINIMAL SURFACES 161 6.4 STABLE CONE AND BERNSTEIN S
PROBLEM 168 6.5 CURVATURE ESTIMATES FOR MINIMAL HYPERSURFACES 176 6.6
EXERCISES 186 CHAPTER VII. BERNSTEIN TYPE THEOREMS FOR HIGHER
CODIMENSION 187 7.1 GEOMETRY OF GRASSMANNIAN MANIFOLDS 188 7.2 HARMONIC
GAUSS MAPS 207 7.3 BERNSTEIN TYPE THEOREMS 214 CHAPTER VIII. ENTIRE
SPACE-LIKE SUBMANIFOLDS 221 8.1 A BOCHNER TYPE FORMULA 224 8.2 THE GAUSS
IMAGE 227 8.3 ESTIMATES OF THE SECOND FUNDAMENTAL FORM 233 8.4
COMPLETENESS 237 8.5 BERNSTEIN S PROBLEM 244 8.6 FINAL REMARKS 250
REFERENCES 251 INDEX 259
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| any_adam_object | 1 |
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| author_facet | Xin, Yuanlong |
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| author_sort | Xin, Yuanlong |
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| building | Verbundindex |
| bvnumber | BV019345151 |
| classification_rvk | SK 370 |
| ctrlnum | (OCoLC)249402989 (DE-599)BVBBV019345151 |
| discipline | Mathematik |
| format | Book |
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| id | DE-604.BV019345151 |
| illustrated | Illustrated |
| indexdate | 2024-07-09T19:58:07Z |
| institution | BVB |
| isbn | 9812386874 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-012809519 |
| oclc_num | 249402989 |
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| owner | DE-703 DE-384 DE-824 DE-11 |
| owner_facet | DE-703 DE-384 DE-824 DE-11 |
| physical | VIII, 262 S. graph. Darst. |
| publishDate | 2003 |
| publishDateSearch | 2003 |
| publishDateSort | 2003 |
| publisher | World Scientific |
| record_format | marc |
| series | Nankai tracts in mathematics |
| series2 | Nankai tracts in mathematics |
| spelling | Xin, Yuanlong Verfasser aut Minimal submanifolds and related topics Yuanlong Xin New Jersey [u.a.] World Scientific 2003 VIII, 262 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Nankai tracts in mathematics 8 Minimale Untermannigfaltigkeit (DE-588)4338425-0 gnd rswk-swf Minimale Untermannigfaltigkeit (DE-588)4338425-0 s DE-604 Nankai tracts in mathematics 8 (DE-604)BV014017593 8 GBV Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=012809519&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Xin, Yuanlong Minimal submanifolds and related topics Nankai tracts in mathematics Minimale Untermannigfaltigkeit (DE-588)4338425-0 gnd |
| subject_GND | (DE-588)4338425-0 |
| title | Minimal submanifolds and related topics |
| title_auth | Minimal submanifolds and related topics |
| title_exact_search | Minimal submanifolds and related topics |
| title_full | Minimal submanifolds and related topics Yuanlong Xin |
| title_fullStr | Minimal submanifolds and related topics Yuanlong Xin |
| title_full_unstemmed | Minimal submanifolds and related topics Yuanlong Xin |
| title_short | Minimal submanifolds and related topics |
| title_sort | minimal submanifolds and related topics |
| topic | Minimale Untermannigfaltigkeit (DE-588)4338425-0 gnd |
| topic_facet | Minimale Untermannigfaltigkeit |
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