Selected topics in convex geometry:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English Polish |
| Veröffentlicht: |
Boston [u.a.]
Birkhäuser
2006
|
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | Aus dem Poln. übers. Literaturverz. S. 217 - 220 |
| Beschreibung: | XVI, 226 S. Illustrationen, Diagramme |
| ISBN: | 0817643966 9780817643966 |
Internformat
MARC
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| 240 | 1 | 0 | |a Geometria zbiorów wypukłych, zagadnienia wybrane |
| 245 | 1 | 0 | |a Selected topics in convex geometry |c Maria Moszyńska |
| 264 | 1 | |a Boston [u.a.] |b Birkhäuser |c 2006 | |
| 300 | |a XVI, 226 S. |b Illustrationen, Diagramme | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 500 | |a Aus dem Poln. übers. | ||
| 500 | |a Literaturverz. S. 217 - 220 | ||
| 650 | 7 | |a Convexe functies |2 gtt | |
| 650 | 7 | |a Convexe ruimten |2 gtt | |
| 650 | 4 | |a Géométrie convexe | |
| 650 | 7 | |a Meetkunde |2 gtt | |
| 650 | 4 | |a Convex geometry | |
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Datensatz im Suchindex
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| adam_text | Contents Preface to the Polish Edition............................................................................... ix Preface to the English Edition............................................................................. xi Introduction................................................................................................................ xiii Part I 1 Metric Spaces ................................................................................................. 1.1 1.2 2 3 3 6 11 The Minkowski operations................................................................ 11 Support hyperplane. The width........................................................ 14 Convex sets ........................................................................................ 18 Compact convex sets. Convex bodies.............................................. 19 Hyperplanes........................................................................................ 20 Subsets of Euclidean Space......................................................................... 2.1 2.2 2.3 2.4 2.5 3 Distance of point and set. Generalized balls.................................... The Hausdorff metric........................................................................ Basic Properties of Convex Sets ................................................................ 25 3.1 3.2 3.3 3.4 Convex combinations........................................................................ Convex hull........................................................................................ Metric
projection................................................................................ Support function................................................................................ 25 28 31 34
vi 4 Contents Transformations of the Space K.n of Compact Convex Sets............... 39 4.1 Isometries and similarities............................................................. 4.2 Symmetrizations of convex sets. The Steiner symmetrization .... 4.3 Other symmetrizations.................................................................. 4.4 Means of rotations......................................................................... 5 Rounding Theorems................................................................................... 53 5.1 The first rounding theorem............................................................ 53 5.2 5.3 5.4 6 Applications of the first rounding theorem.................................... 55 The second rounding theorem...................................................... 56 Applications of the second rounding theorem.............................. 58 Convex Polytopes ........................................................................................ 61 6.1 Polyhedra and their role in topology............................................. 61 6.2 6.3 6.4 6.5 7 39 41 48 49 Convex polytopes......................................................................... Approximation of convex bodies by polytopes............................ Equivalence by dissection ............................................................ Spherical polytopes....................................................................... 64 67 69 71 Functionals on the Space /C . The Steiner Theorem............................ 73 7.1 7.2 7.3 Functionals on the space A
........................................................ 73 Basic functionals. The Steiner theorem......................................... 77 Consequences of the Steiner theorem........................................... 82 8 The Hadwiger Theorems.......................................................................... 89 8.1 The first Hadwiger theorem.......................................................... 89 8.2 The second Hadwiger theorem .................................................... 95 9 Applications of the Hadwiger Theorems............................................... 97 9.1 Mean width and mean curvature.................................................. 97 9.2 The Crofton formulae................................................................... 98 9.3 The Cauchy formulae..................................................................... 102 Partii__________________________________________________ ___________ 10 Curvature and Surface Area Measures................................................... 109 10.1 Curvature measures........................................................................... 109 10.2 Surface area measures........................................................................117 10.3 Curvature and surface area measures for smooth, strictly convex bodies...............................................................................................120 11 Sets with Positive Reach. Convexity Ring .............................................. 125 11.1 Sets with positive reach
.................................................................... 125 11.2 Convexity ring................................................................................... 127
Contents vii 12 Selectors for Convex Bodies................................................................... 135 12.1 Symmetry centers............................................................................ 135 12.2 Selectors and multiselectors............................................................ 137 12.3 Centers of gravity ............................................................................138 12.4 The Steiner point..............................................................................142 12.5 Center of the minimal ring.............................................................. 144 12.6 Pseudocenter. G-pseudocenters....................................................... 149 12.7 G-quasi-centers. Chebyshev point................................................... 154 13 Polarity..................................................................................................... 159 13.1 Polar hyperplane of a point with respectto the unit sphere ............ 159 13.2 Polarity for arbitrary subsets of R”................................................. 161 13.3 Polarity for convex bodies.............................................................. 163 13.4 Combinatorial duality induced by polarity...................................... 165 13.5 Santaló point................................................................................... 166 13.6 Self-duality of the center of the minimalring ................................. 168 13.7 Metric polarity................................................................................. 169 Partili 14
Star 14.1 14.2 14.3 14.4 15 Sets. Star Bodies........................................................................... 175 Star sets. Radialfunction................................................................ 175 Star bodies......................................................................................177 Radial metric.................................................................................. 179 Star metric...................................................................................... 181 Intersection Bodies................................................................................. 185 15.1 Dual intrinsic volumes.................................................................... 185 15.2 Projection bodies of convex bodies. The Shephard problem ..........186 15.3 Intersection bodies of star bodies. The Busemann-Petty problem. 187 15.4 Star duality....................................................................................... 189 16 Selectors for Star Bodies ....................................................................... 193 16.1 Radial centers of a star body ...........................................................193 16.2 Radial centers of a convex body ..................................................... 195 16.3 Extended radial centers of a star body............................................. 198 Exercises to Part I.................................................................................. 203 Exercises to Part II.................................................................................211 Exercises to
Part III...............................................................................215 References.............................................................................................. 217
viii Contents List of Symbois........................................................................................... 221 Index.............................................................................................................. 223
|
| adam_txt |
Contents Preface to the Polish Edition. ix Preface to the English Edition. xi Introduction. xiii Part I 1 Metric Spaces . 1.1 1.2 2 3 3 6 11 The Minkowski operations. 11 Support hyperplane. The width. 14 Convex sets . 18 Compact convex sets. Convex bodies. 19 Hyperplanes. 20 Subsets of Euclidean Space. 2.1 2.2 2.3 2.4 2.5 3 Distance of point and set. Generalized balls. The Hausdorff metric. Basic Properties of Convex Sets . 25 3.1 3.2 3.3 3.4 Convex combinations. Convex hull. Metric
projection. Support function. 25 28 31 34
vi 4 Contents Transformations of the Space K.n of Compact Convex Sets. 39 4.1 Isometries and similarities. 4.2 Symmetrizations of convex sets. The Steiner symmetrization . 4.3 Other symmetrizations. 4.4 Means of rotations. 5 Rounding Theorems. 53 5.1 The first rounding theorem. 53 5.2 5.3 5.4 6 Applications of the first rounding theorem. 55 The second rounding theorem. 56 Applications of the second rounding theorem. 58 Convex Polytopes . 61 6.1 Polyhedra and their role in topology. 61 6.2 6.3 6.4 6.5 7 39 41 48 49 Convex polytopes. Approximation of convex bodies by polytopes. Equivalence by dissection . Spherical polytopes. 64 67 69 71 Functionals on the Space /C". The Steiner Theorem. 73 7.1 7.2 7.3 Functionals on the space A"
. 73 Basic functionals. The Steiner theorem. 77 Consequences of the Steiner theorem. 82 8 The Hadwiger Theorems. 89 8.1 The first Hadwiger theorem. 89 8.2 The second Hadwiger theorem . 95 9 Applications of the Hadwiger Theorems. 97 9.1 Mean width and mean curvature. 97 9.2 The Crofton formulae. 98 9.3 The Cauchy formulae. 102 Partii_ _ 10 Curvature and Surface Area Measures. 109 10.1 Curvature measures. 109 10.2 Surface area measures.117 10.3 Curvature and surface area measures for smooth, strictly convex bodies.120 11 Sets with Positive Reach. Convexity Ring . 125 11.1 Sets with positive reach
. 125 11.2 Convexity ring. 127
Contents vii 12 Selectors for Convex Bodies. 135 12.1 Symmetry centers. 135 12.2 Selectors and multiselectors. 137 12.3 Centers of gravity .138 12.4 The Steiner point.142 12.5 Center of the minimal ring. 144 12.6 Pseudocenter. G-pseudocenters. 149 12.7 G-quasi-centers. Chebyshev point. 154 13 Polarity. 159 13.1 Polar hyperplane of a point with respectto the unit sphere . 159 13.2 Polarity for arbitrary subsets of R”. 161 13.3 Polarity for convex bodies. 163 13.4 Combinatorial duality induced by polarity. 165 13.5 Santaló point. 166 13.6 Self-duality of the center of the minimalring . 168 13.7 Metric polarity. 169 Partili 14
Star 14.1 14.2 14.3 14.4 15 Sets. Star Bodies. 175 Star sets. Radialfunction. 175 Star bodies.177 Radial metric. 179 Star metric. 181 Intersection Bodies. 185 15.1 Dual intrinsic volumes. 185 15.2 Projection bodies of convex bodies. The Shephard problem .186 15.3 Intersection bodies of star bodies. The Busemann-Petty problem. 187 15.4 Star duality. 189 16 Selectors for Star Bodies . 193 16.1 Radial centers of a star body .193 16.2 Radial centers of a convex body . 195 16.3 Extended radial centers of a star body. 198 Exercises to Part I. 203 Exercises to Part II.211 Exercises to
Part III.215 References. 217
viii Contents List of Symbois. 221 Index. 223 |
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| author | Moszyńska, Maria |
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| dewey-full | 516/.08 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 516 - Geometry |
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| dewey-search | 516/.08 |
| dewey-sort | 3516 18 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| discipline_str_mv | Mathematik |
| format | Book |
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| illustrated | Illustrated |
| index_date | 2024-07-02T19:16:30Z |
| indexdate | 2024-07-09T21:09:22Z |
| institution | BVB |
| isbn | 0817643966 9780817643966 |
| language | English Polish |
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| physical | XVI, 226 S. Illustrationen, Diagramme |
| publishDate | 2006 |
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| spelling | Moszyńska, Maria Verfasser (DE-588)130606731 aut Geometria zbiorów wypukłych, zagadnienia wybrane Selected topics in convex geometry Maria Moszyńska Boston [u.a.] Birkhäuser 2006 XVI, 226 S. Illustrationen, Diagramme txt rdacontent n rdamedia nc rdacarrier Aus dem Poln. übers. Literaturverz. S. 217 - 220 Convexe functies gtt Convexe ruimten gtt Géométrie convexe Meetkunde gtt Convex geometry Konvexe Geometrie (DE-588)4407260-0 gnd rswk-swf Konvexe Geometrie (DE-588)4407260-0 s b DE-604 Erscheint auch als Online-Ausgabe 0-8176-4451-2 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=016233667&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Moszyńska, Maria Selected topics in convex geometry Convexe functies gtt Convexe ruimten gtt Géométrie convexe Meetkunde gtt Convex geometry Konvexe Geometrie (DE-588)4407260-0 gnd |
| subject_GND | (DE-588)4407260-0 |
| title | Selected topics in convex geometry |
| title_alt | Geometria zbiorów wypukłych, zagadnienia wybrane |
| title_auth | Selected topics in convex geometry |
| title_exact_search | Selected topics in convex geometry |
| title_exact_search_txtP | Selected topics in convex geometry |
| title_full | Selected topics in convex geometry Maria Moszyńska |
| title_fullStr | Selected topics in convex geometry Maria Moszyńska |
| title_full_unstemmed | Selected topics in convex geometry Maria Moszyńska |
| title_short | Selected topics in convex geometry |
| title_sort | selected topics in convex geometry |
| topic | Convexe functies gtt Convexe ruimten gtt Géométrie convexe Meetkunde gtt Convex geometry Konvexe Geometrie (DE-588)4407260-0 gnd |
| topic_facet | Convexe functies Convexe ruimten Géométrie convexe Meetkunde Convex geometry Konvexe Geometrie |
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