Lectures on convex geometry:
Gespeichert in:
| Hauptverfasser: | , |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Cham, Switzerland
Springer
[2020]
|
| Schriftenreihe: | Graduate texts in mathematics
286 |
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | xviii, 287 Seiten Illustrationen, Diagramme |
| ISBN: | 9783030501792 |
Internformat
MARC
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| 300 | |a xviii, 287 Seiten |b Illustrationen, Diagramme | ||
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| 490 | 1 | |a Graduate texts in mathematics |v 286 | |
| 650 | 4 | |a Convex and Discrete Geometry | |
| 650 | 4 | |a Polytopes | |
| 650 | 4 | |a Measure and Integration | |
| 650 | 4 | |a Functional Analysis | |
| 650 | 4 | |a Convex geometry | |
| 650 | 4 | |a Discrete geometry | |
| 650 | 4 | |a Polytopes | |
| 650 | 4 | |a Measure theory | |
| 650 | 4 | |a Functional analysis | |
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| 830 | 0 | |a Graduate texts in mathematics |v 286 |w (DE-604)BV000000067 |9 286 | |
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Datensatz im Suchindex
| _version_ | 1804181768783265792 |
|---|---|
| adam_text | Contents 1 Convex Sets........................................................................................................ 1.1 1.2 1.3 1.4 1.5 2 Algebraic Properties.............................................................................. Combinatorial Properties....................................................................... Topological Properties........................................................................... Support and Separation.......................................................................... Extremal Representations....................................................................... Convex Functions............................................................................................. 2.1 PropertiesandOperations...................................................................... 2.2 Regularity............................................................................................... 2.3 The Support Function............................................................................. 3 73 The Space of Convex Bodies................................................................. 73 Volume and Surface Area....................................................................... 86 Mixed Volumes....................................................................................... 93 The Brunn-Minkowski Theorem.......................................................... 115 The Alexandrov-Fenchel Inequality.................................................... 126 Steiner
Symmetrization.......................................................................... 136 From Area Measures to Valuations............................................................. 4.1 4.2 4.3 4.4 4.5 5 41 41 52 61 Brunn-Minkowski Theory............................................................................. 3.1 3.2 3.3 3.4 3.5 3.6 4 1 1 12 17 23 33 Mixed Area Measures............................................................................. An Existence and Uniqueness Result................................................... A Local Steiner Formula........................................................................ Projection Bodies and Zonoids.............................................................. Valuations............................................................................................... Integral-Geometric Formulas....................................................................... 5.1 5.2 5.3 5.4 Invariant Measures................................................................................. Projection Formulas................................................................................ Section Formulas.................................................................................... Kinematic Formulas.............................................................................. 147 148 156 169 179 196 207 208 221 226 233 xi
xii Contents Solutions of Selected Exercises............................................................... 6.1 Solutions of Exercises for Chap. 1 ..................................................... 6.2 Solutions of Exercises for Chap. 2..................................................... 6.3 Solutions of Exercises for Chap. 3..................................................... 6.4 Solutions of Exercises for Chap. 4..................................................... 6.5 Solutions of Exercises for Chap. 5..................................................... 239 239 249 256 268 278 References....................................................................................................... 281 6 Index................................................................................................................ 285
|
| adam_txt |
Contents 1 Convex Sets. 1.1 1.2 1.3 1.4 1.5 2 Algebraic Properties. Combinatorial Properties. Topological Properties. Support and Separation. Extremal Representations. Convex Functions. 2.1 PropertiesandOperations. 2.2 Regularity. 2.3 The Support Function. 3 73 The Space of Convex Bodies. 73 Volume and Surface Area. 86 Mixed Volumes. 93 The Brunn-Minkowski Theorem. 115 The Alexandrov-Fenchel Inequality. 126 Steiner
Symmetrization. 136 From Area Measures to Valuations. 4.1 4.2 4.3 4.4 4.5 5 41 41 52 61 Brunn-Minkowski Theory. 3.1 3.2 3.3 3.4 3.5 3.6 4 1 1 12 17 23 33 Mixed Area Measures. An Existence and Uniqueness Result. A Local Steiner Formula. Projection Bodies and Zonoids. Valuations. Integral-Geometric Formulas. 5.1 5.2 5.3 5.4 Invariant Measures. Projection Formulas. Section Formulas. Kinematic Formulas. 147 148 156 169 179 196 207 208 221 226 233 xi
xii Contents Solutions of Selected Exercises. 6.1 Solutions of Exercises for Chap. 1 . 6.2 Solutions of Exercises for Chap. 2. 6.3 Solutions of Exercises for Chap. 3. 6.4 Solutions of Exercises for Chap. 4. 6.5 Solutions of Exercises for Chap. 5. 239 239 249 256 268 278 References. 281 6 Index. 285 |
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| author | Hug, Daniel 1965- Weil, Wolfgang 1945-2018 |
| author_GND | (DE-588)1218035226 (DE-588)1015070035 |
| author_facet | Hug, Daniel 1965- Weil, Wolfgang 1945-2018 |
| author_role | aut aut |
| author_sort | Hug, Daniel 1965- |
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| ctrlnum | (OCoLC)1197075529 (DE-599)BVBBV046898802 |
| dewey-full | 516.1 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 516 - Geometry |
| dewey-raw | 516.1 |
| dewey-search | 516.1 |
| dewey-sort | 3516.1 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| discipline_str_mv | Mathematik |
| format | Book |
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| illustrated | Illustrated |
| index_date | 2024-07-03T15:23:32Z |
| indexdate | 2024-07-10T08:56:54Z |
| institution | BVB |
| isbn | 9783030501792 |
| language | English |
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| physical | xviii, 287 Seiten Illustrationen, Diagramme |
| publishDate | 2020 |
| publishDateSearch | 2020 |
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| series | Graduate texts in mathematics |
| series2 | Graduate texts in mathematics |
| spelling | Hug, Daniel 1965- Verfasser (DE-588)1218035226 aut Lectures on convex geometry Daniel Hug, Wolfgang Weil Cham, Switzerland Springer [2020] xviii, 287 Seiten Illustrationen, Diagramme txt rdacontent n rdamedia nc rdacarrier Graduate texts in mathematics 286 Convex and Discrete Geometry Polytopes Measure and Integration Functional Analysis Convex geometry Discrete geometry Measure theory Functional analysis Konvexe Geometrie (DE-588)4407260-0 gnd rswk-swf Konvexe Geometrie (DE-588)4407260-0 s DE-604 Weil, Wolfgang 1945-2018 Verfasser (DE-588)1015070035 aut Erscheint auch als Online-Ausgabe 978-3-030-50180-8 Graduate texts in mathematics 286 (DE-604)BV000000067 286 Digitalisierung UB Passau - ADAM Catalogue Enrichment application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=032308501&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Hug, Daniel 1965- Weil, Wolfgang 1945-2018 Lectures on convex geometry Graduate texts in mathematics Convex and Discrete Geometry Polytopes Measure and Integration Functional Analysis Convex geometry Discrete geometry Measure theory Functional analysis Konvexe Geometrie (DE-588)4407260-0 gnd |
| subject_GND | (DE-588)4407260-0 |
| title | Lectures on convex geometry |
| title_auth | Lectures on convex geometry |
| title_exact_search | Lectures on convex geometry |
| title_exact_search_txtP | Lectures on convex geometry |
| title_full | Lectures on convex geometry Daniel Hug, Wolfgang Weil |
| title_fullStr | Lectures on convex geometry Daniel Hug, Wolfgang Weil |
| title_full_unstemmed | Lectures on convex geometry Daniel Hug, Wolfgang Weil |
| title_short | Lectures on convex geometry |
| title_sort | lectures on convex geometry |
| topic | Convex and Discrete Geometry Polytopes Measure and Integration Functional Analysis Convex geometry Discrete geometry Measure theory Functional analysis Konvexe Geometrie (DE-588)4407260-0 gnd |
| topic_facet | Convex and Discrete Geometry Polytopes Measure and Integration Functional Analysis Convex geometry Discrete geometry Measure theory Functional analysis Konvexe Geometrie |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=032308501&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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