Convex bodies: the Brunn-Minkowski theory
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Cambridge [u.a.]
Cambridge Univ. Press
2014
|
| Ausgabe: | 2., expanded ed. |
| Schriftenreihe: | Encyclopedia of mathematics and its applications
151 |
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | Literaturverz. S. [629] - 714 |
| Beschreibung: | XXII, 736 S. |
| ISBN: | 9781107601017 |
Internformat
MARC
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| 245 | 1 | 0 | |a Convex bodies |b the Brunn-Minkowski theory |c Rolf Schneider |
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| 300 | |a XXII, 736 S. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 490 | 1 | |a Encyclopedia of mathematics and its applications |v 151 | |
| 500 | |a Literaturverz. S. [629] - 714 | ||
| 650 | 0 | 7 | |a Konvexer Körper |0 (DE-588)4165214-9 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Brunn-Minkowski-Satz |0 (DE-588)4333020-4 |2 gnd |9 rswk-swf |
| 689 | 0 | 0 | |a Konvexer Körper |0 (DE-588)4165214-9 |D s |
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Datensatz im Suchindex
| _version_ | 1804151775732695040 |
|---|---|
| adam_text | 0
e ix
xi
XV
xix
1
1
9
11
15
19
32
44
60
74
74
81
90
104
112
126
132
139
139
156
172
183
189
Contents
Preface to the second edition
Preface to the first edition
General hints to the literature
Conventions and notation
Basic convexity
1.1 Convex sets and combinations
1.2 The metric projection
1.3 Support and separation
1.4 Extremal representations
1.5 Convex functions
1.6 Duality
1.7 Functions representing convex sets
1.8 The HausdorfF metric
Boundary structure
2.1 Facial structure
2.2 Singularities
2.3 Segments in the boundary
2.4 Polytopes
2.5 Higher regularity and curvature
2.6 Generalized curvatures
2.7 Generic boundary structure
Minkowski addition
3.1 Minkowski addition and subtraction
3.2 Summands and decomposition
3.3 Additive maps
3.4 Approximation and addition
3.5 Minkowski classes and additive generation
Support measures and intrinsic volumes
4.1 Local parallel sets
Contents
vi
4.2 Steiner formula and support measures 211
4.3 Extensions of support measures 228
4.4 Integral-geometric formulae 236
4.5 Local behaviour of curvature and area measures 265
5 Mixed volumes and related concepts 275
5.1 Mixed volumes and mixed area measures 275
5.2 Extensions of mixed volumes 290
5.3 Special formulae for mixed volumes 295
5.4 Moment vectors, curvature centroids, Minkowski tensors 312
5.5 Mixed discriminants 322
6 Valuations on convex bodies 329
6.1 Basic facts and examples 329
6.2 Extensions 332
6.3 Polynomiality 340
6.4 Translation invariant, continuous valuations 346
6.5 The modern theory of valuations 365
7 Inequalities for mixed volumes 369
7.1 The Brunn-Minkowski theorem 369
7.2 The Minkowski and isoperimetric inequalities 381
7.3 The Aleksandrov-Fenchel inequality 393
7.4 Consequences and improvements 399
7.5 Wulff shapes 410
7.6 Equality cases and stability 418
7.7 Linear inequalities 440
8 Determination by area measures and curvatures 447
8.1 Uniqueness results 447
8.2 Convex bodies with given surface area measures 455
8.3 The area measure of order one 464
8.4 The intermediate area measures 473
8.5 Stability and further uniqueness results 478
9 Extensions and analogues of the Brunn-Minkowski theory 489
9.1 The Lp Brunn-Minkowski theory 489
9.2 The Lp Minkowski problem and generalizations 498
9.3 The dual Brunn-Minkowski theory 507
9.4 Further combinations and functionals 512
9.5 Log-concave functions and generalizations 516
9.6 A glimpse of other ramifications 525
10 Affine constructions and inequalities 528
10.1 Covariogram and difference body 528
10.2 Qualitative characterizations of ellipsoids 535
10.3 Steiner symmetrization 536
Contents vii
10.4 Shadow systems 541
10.5 Curvature images and affine surface areas 543
10.6 Floating bodies and similar constructions 560
10.7 The volume product 563
10.8 Moment bodies and centroid bodies 566
10.9 Projection bodies 569
10.10 Intersection bodies 580
10.11 Volume comparison 583
10.12 Associated ellipsoids 587
10.13 Isotropic measures, special positions, reverse inequalities 595
10.14 Lp zonoids 606
10.15 From geometric to analytic inequalities 610
10.16 Characterization theorems 614
Appendix Spherical harmonics 623
References 629
Notation index 715
Audio r index 119
Subject index 729
|
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| discipline | Mathematik |
| edition | 2., expanded ed. |
| format | Book |
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| id | DE-604.BV041584969 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-10T01:00:11Z |
| institution | BVB |
| isbn | 9781107601017 |
| language | English |
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| physical | XXII, 736 S. |
| publishDate | 2014 |
| publishDateSearch | 2014 |
| publishDateSort | 2014 |
| publisher | Cambridge Univ. Press |
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| series | Encyclopedia of mathematics and its applications |
| series2 | Encyclopedia of mathematics and its applications |
| spelling | Schneider, Rolf 1940- Verfasser (DE-588)129512877 aut Convex bodies the Brunn-Minkowski theory Rolf Schneider 2., expanded ed. Cambridge [u.a.] Cambridge Univ. Press 2014 XXII, 736 S. txt rdacontent n rdamedia nc rdacarrier Encyclopedia of mathematics and its applications 151 Literaturverz. S. [629] - 714 Konvexer Körper (DE-588)4165214-9 gnd rswk-swf Brunn-Minkowski-Satz (DE-588)4333020-4 gnd rswk-swf Konvexer Körper (DE-588)4165214-9 s Brunn-Minkowski-Satz (DE-588)4333020-4 s DE-604 Encyclopedia of mathematics and its applications 151 (DE-604)BV000903719 151 Digitalisierung UB Bayreuth - ADAM Catalogue Enrichment application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=027030155&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Schneider, Rolf 1940- Convex bodies the Brunn-Minkowski theory Encyclopedia of mathematics and its applications Konvexer Körper (DE-588)4165214-9 gnd Brunn-Minkowski-Satz (DE-588)4333020-4 gnd |
| subject_GND | (DE-588)4165214-9 (DE-588)4333020-4 |
| title | Convex bodies the Brunn-Minkowski theory |
| title_auth | Convex bodies the Brunn-Minkowski theory |
| title_exact_search | Convex bodies the Brunn-Minkowski theory |
| title_full | Convex bodies the Brunn-Minkowski theory Rolf Schneider |
| title_fullStr | Convex bodies the Brunn-Minkowski theory Rolf Schneider |
| title_full_unstemmed | Convex bodies the Brunn-Minkowski theory Rolf Schneider |
| title_short | Convex bodies |
| title_sort | convex bodies the brunn minkowski theory |
| title_sub | the Brunn-Minkowski theory |
| topic | Konvexer Körper (DE-588)4165214-9 gnd Brunn-Minkowski-Satz (DE-588)4333020-4 gnd |
| topic_facet | Konvexer Körper Brunn-Minkowski-Satz |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=027030155&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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