The geometry of domains in space:
Gespeichert in:
| Hauptverfasser: | , |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Boston [u.a.]
Birkhäuser
1999
|
| Schriftenreihe: | Birkhäuser advanced texts
|
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | X, 308 S. graph. Darst. |
| ISBN: | 0817640975 3764340975 9780817640972 |
Internformat
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Datensatz im Suchindex
| _version_ | 1804127081569714176 |
|---|---|
| adam_text | STEVEN G. KRANTZ HAROLD R. PARKS THE GEOMETRY OF DOMAINS IN SPACE
BIRKHAUSER BOSTON * BASEL * BERLIN CONTENTS PREFACE IX 1. ELEMENTARY
TOPICS 1 1.1 SMOOTH FUNCTIONS 1 1.2 THE CONCEPT OF DENNING FUNCTION 8
1.3 MEASURE THEORY 15 2. DOMAINS WITH SMOOTH BOUNDARIES 27 2.1 THE
TANGENT BUNDLE AND NORMAL BUNDLE OF THE BOUNDARY 27 2.2 THE SECOND
FUNDAMENTAL FORM AND CURVATURE 34 2.3 SURFACES WITH CONSTANT MEAN
CURVATURE 45 3. MEASURES 57 3.1 THE CARATHEODORY CONSTRUCTION 57 3.2
RECTIFIABILITY 66 3.3 MINKOWSKI CONTENT 74 3.4 A SPACE-FILLING CURVE 81
3.5 COVERING LEMMAS 83 3.6 FUNCTIONS OF BOUNDED VARIATION 100 3.7
DOMAINS WITH FINITE PERIMETER 107 3.8 THE AREA FORMULA 123 3.9 THE
CO-AREA FORMULA 136 4. SOBOLEV SPACES 143 4.1 BASIC DEFINITIONS AND
RESULTS 143 4.2 RESTRICTION AND TRACE THEOREMS FOR SOBOLEV SPACES 148
4.3 DOMAIN EXTENSION THEOREMS FOR SOBOLEV SPACES 153 VIII CONTENTS 5.
SMOOTH MAPPINGS 157 5.1 SARD S THEOREM 157 5.2 EXTENSION THEOREMS 162
5.3 PROOF OF THE WHITNEY EXTENSION THEOREM 167 5.4 APPLICATION OF THE
WHITNEY EXTENSION THEOREM 179 5.5 MULTIDIMENSIONAL VERSIONS OF THE
FUNDAMENTAL THEOREM OF CALCULUS 183 6. CONVEXITY 191 6.1 THE CLASSICAL
NOTION OF CONVEXITY 191 6.2 OTHER CHARACTERIZATIONS OF CONVEXITY 201 6.3
EXHAUSTION FUNCTIONS 211 6.4 CONVEXITY OF ORDER K 217 7. STEINER
SYMMETRIZATION 223 7.1 BASIC PROPERTIES 223 7.2 THE ISODIAMETRIC,
ISOPERIMETRIC AND BRUNN-MINKOWSKI INEQUALITIES 231 7.3 EQUALITY IN THE
ISOPERIMETRIC INEQUALITY 243 8. TOPICS RELATED TO COMPLEX ANALYSIS 247
8.1 QUASICONFORMAL MAPPINGS 247 8.2 WEYL S THEOREM ON EIGENVALUE
ASYMPTOTICS OF A DOMAIN IN SPACE 259 A.I. METRICS ON THE COLLECTION OF
SUBSETS OF EUCLIDEAN SPACE 275 A.2. THE CONSTANTS ASSOCIATED TO
EUCLIDEAN SPACE 281 GUIDE TO NOTATION 287 BIBLIOGRAPHY 291 INDEX 305
|
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| indexdate | 2024-07-09T18:27:41Z |
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| isbn | 0817640975 3764340975 9780817640972 |
| language | English |
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| physical | X, 308 S. graph. Darst. |
| publishDate | 1999 |
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| spelling | Krantz, Steven G. 1951- Verfasser (DE-588)130535907 aut The geometry of domains in space Steven G. Krantz ; Harold R. Parks Boston [u.a.] Birkhäuser 1999 X, 308 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Birkhäuser advanced texts Analyse mathématique Géométrie Geometry Mathematical analysis Geometrische Analysis (DE-588)4156708-0 gnd rswk-swf Geometrische Analysis (DE-588)4156708-0 s DE-604 Parks, Harold R. Verfasser aut GBV Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=008444009&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Krantz, Steven G. 1951- Parks, Harold R. The geometry of domains in space Analyse mathématique Géométrie Geometry Mathematical analysis Geometrische Analysis (DE-588)4156708-0 gnd |
| subject_GND | (DE-588)4156708-0 |
| title | The geometry of domains in space |
| title_auth | The geometry of domains in space |
| title_exact_search | The geometry of domains in space |
| title_full | The geometry of domains in space Steven G. Krantz ; Harold R. Parks |
| title_fullStr | The geometry of domains in space Steven G. Krantz ; Harold R. Parks |
| title_full_unstemmed | The geometry of domains in space Steven G. Krantz ; Harold R. Parks |
| title_short | The geometry of domains in space |
| title_sort | the geometry of domains in space |
| topic | Analyse mathématique Géométrie Geometry Mathematical analysis Geometrische Analysis (DE-588)4156708-0 gnd |
| topic_facet | Analyse mathématique Géométrie Geometry Mathematical analysis Geometrische Analysis |
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