Convex bodies :: the Brunn-Minkowski theory /
"At the heart of this monograph is the Brunn-Minkowski theory. It can be used to great effect in studying such ideas as volume and surface area and the generalizations of these. In particular the notions of mixed volume and mixed area arise naturally and the fundamental inequalities that are sa...
Gespeichert in:
| 1. Verfasser: | |
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| Format: | Elektronisch E-Book |
| Sprache: | English |
| Veröffentlicht: |
Cambridge ; New York :
Cambridge University Press,
[1993]
|
| Schriftenreihe: | Encyclopedia of mathematics and its applications ;
v. 44. |
| Schlagworte: | |
| Online-Zugang: | Volltext |
| Zusammenfassung: | "At the heart of this monograph is the Brunn-Minkowski theory. It can be used to great effect in studying such ideas as volume and surface area and the generalizations of these. In particular the notions of mixed volume and mixed area arise naturally and the fundamental inequalities that are satisfied by mixed volumes are considered in detail." "The author presents a comprehensive introduction to convex bodies and gives full proofs for some deeper theorems which have never previously been brought together. Many hints and pointers to connections with other fields are given, and an exhaustive reference list is included."--Jacket |
| Beschreibung: | 1 online resource (xiii, 490 pages) : illustrations |
| Bibliographie: | Includes bibliographical references (pages 433-473) and index. |
| ISBN: | 9781107087941 1107087945 1139884360 9781139884365 1107102618 9781107102613 1107094151 9781107094154 0511526288 9780511526282 |
Internformat
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| 504 | |a Includes bibliographical references (pages 433-473) and index. | ||
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| 588 | 0 | |a Print version record. | |
| 505 | 0 | |a Cover; Half-title; Title; Copyright; Contents; Preface; Conventions and notation; 1 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 The support function; 1.8 The Hausdorff metric; 2 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 Generic boundary structure; 3 Minkowski addition; 3.1 Minkowski addition and subtraction; 3.2 Summands and decomposition | |
| 505 | 8 | |a 3.3 Approximation and addition3.4 Additive maps; 3.5 Zonoids and other classes of convex bodies; 4 Curvature measures and quermassintegrals; 4.1 Local parallel sets; 4.2 Curvature measures and area measures; 4.3 The area measure of order one; 4.4 Additive extension; 4.5 Integral-geometric formulae; 4.6 Local behaviour of curvature measures; 5 Mixed volumes and related concepts; 5.1 Mixed volumes and mixed area measures; 5.2 Extensions of mixed volumes; 5.3 Special formulae for mixed volumes and quermassintegrals; 5.4 Moment vectors and curvature centroids; 6 Inequalities for mixed volumes | |
| 505 | 8 | |a 6.1 The Brunn-Minkowski theorem6.2 The Minkowski and isoperimetric inequalities; 6.3 The Aleksandrov-Fenchel inequality; 6.4 Consequences and improvements; 6.5 Generalized parallel bodies; 6.6 Equality cases and stability; 6.7 Linear inequalities; 6.8 Analogous notions and inequalities; 7 Selected applications; 7.1 Minkowski's existence theorem; 7.2 Uniqueness theorems for area measures; 7.3 The difference-body inequality; 7.4 Affinely associated bodies; Appendix Spherical harmonics; References; List of symbols; Author index; Subject index | |
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| adam_text | |
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| author | Schneider, Rolf, 1940- |
| author_GND | http://id.loc.gov/authorities/names/n92028124 |
| author_facet | Schneider, Rolf, 1940- |
| author_role | |
| author_sort | Schneider, Rolf, 1940- |
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| contents | Cover; Half-title; Title; Copyright; Contents; Preface; Conventions and notation; 1 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 The support function; 1.8 The Hausdorff metric; 2 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 Generic boundary structure; 3 Minkowski addition; 3.1 Minkowski addition and subtraction; 3.2 Summands and decomposition 3.3 Approximation and addition3.4 Additive maps; 3.5 Zonoids and other classes of convex bodies; 4 Curvature measures and quermassintegrals; 4.1 Local parallel sets; 4.2 Curvature measures and area measures; 4.3 The area measure of order one; 4.4 Additive extension; 4.5 Integral-geometric formulae; 4.6 Local behaviour of curvature measures; 5 Mixed volumes and related concepts; 5.1 Mixed volumes and mixed area measures; 5.2 Extensions of mixed volumes; 5.3 Special formulae for mixed volumes and quermassintegrals; 5.4 Moment vectors and curvature centroids; 6 Inequalities for mixed volumes 6.1 The Brunn-Minkowski theorem6.2 The Minkowski and isoperimetric inequalities; 6.3 The Aleksandrov-Fenchel inequality; 6.4 Consequences and improvements; 6.5 Generalized parallel bodies; 6.6 Equality cases and stability; 6.7 Linear inequalities; 6.8 Analogous notions and inequalities; 7 Selected applications; 7.1 Minkowski's existence theorem; 7.2 Uniqueness theorems for area measures; 7.3 The difference-body inequality; 7.4 Affinely associated bodies; Appendix Spherical harmonics; References; List of symbols; Author index; Subject index |
| ctrlnum | (OCoLC)864551999 |
| dewey-full | 516.3/74 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 516 - Geometry |
| dewey-raw | 516.3/74 |
| dewey-search | 516.3/74 |
| dewey-sort | 3516.3 274 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| format | Electronic eBook |
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| id | ZDB-4-EBA-ocn864551999 |
| illustrated | Illustrated |
| indexdate | 2024-11-27T13:25:39Z |
| institution | BVB |
| isbn | 9781107087941 1107087945 1139884360 9781139884365 1107102618 9781107102613 1107094151 9781107094154 0511526288 9780511526282 |
| language | English |
| oclc_num | 864551999 |
| open_access_boolean | |
| owner | MAIN DE-863 DE-BY-FWS |
| owner_facet | MAIN DE-863 DE-BY-FWS |
| physical | 1 online resource (xiii, 490 pages) : illustrations |
| psigel | ZDB-4-EBA |
| publishDate | 1993 |
| publishDateSearch | 1993 |
| publishDateSort | 1993 |
| publisher | Cambridge University Press, |
| record_format | marc |
| series | Encyclopedia of mathematics and its applications ; |
| series2 | Encyclopedia of mathematics and its applications ; |
| spelling | Schneider, Rolf, 1940- https://id.oclc.org/worldcat/entity/E39PBJxMhVVmWxByFjhfTtdhHC http://id.loc.gov/authorities/names/n92028124 Convex bodies : the Brunn-Minkowski theory / Rolf Schneider. Cambridge ; New York : Cambridge University Press, [1993] ©1993 1 online resource (xiii, 490 pages) : illustrations text txt rdacontent computer c rdamedia online resource cr rdacarrier Encyclopedia of mathematics and its applications ; volume 44 Includes bibliographical references (pages 433-473) and index. "At the heart of this monograph is the Brunn-Minkowski theory. It can be used to great effect in studying such ideas as volume and surface area and the generalizations of these. In particular the notions of mixed volume and mixed area arise naturally and the fundamental inequalities that are satisfied by mixed volumes are considered in detail." "The author presents a comprehensive introduction to convex bodies and gives full proofs for some deeper theorems which have never previously been brought together. Many hints and pointers to connections with other fields are given, and an exhaustive reference list is included."--Jacket Print version record. Cover; Half-title; Title; Copyright; Contents; Preface; Conventions and notation; 1 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 The support function; 1.8 The Hausdorff metric; 2 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 Generic boundary structure; 3 Minkowski addition; 3.1 Minkowski addition and subtraction; 3.2 Summands and decomposition 3.3 Approximation and addition3.4 Additive maps; 3.5 Zonoids and other classes of convex bodies; 4 Curvature measures and quermassintegrals; 4.1 Local parallel sets; 4.2 Curvature measures and area measures; 4.3 The area measure of order one; 4.4 Additive extension; 4.5 Integral-geometric formulae; 4.6 Local behaviour of curvature measures; 5 Mixed volumes and related concepts; 5.1 Mixed volumes and mixed area measures; 5.2 Extensions of mixed volumes; 5.3 Special formulae for mixed volumes and quermassintegrals; 5.4 Moment vectors and curvature centroids; 6 Inequalities for mixed volumes 6.1 The Brunn-Minkowski theorem6.2 The Minkowski and isoperimetric inequalities; 6.3 The Aleksandrov-Fenchel inequality; 6.4 Consequences and improvements; 6.5 Generalized parallel bodies; 6.6 Equality cases and stability; 6.7 Linear inequalities; 6.8 Analogous notions and inequalities; 7 Selected applications; 7.1 Minkowski's existence theorem; 7.2 Uniqueness theorems for area measures; 7.3 The difference-body inequality; 7.4 Affinely associated bodies; Appendix Spherical harmonics; References; List of symbols; Author index; Subject index English. Convex bodies. http://id.loc.gov/authorities/subjects/sh85031726 Corps convexes. MATHEMATICS Geometry General. bisacsh Convex bodies fast Konvexer Körper gnd http://d-nb.info/gnd/4165214-9 Corps convexes. ram Géométrie analytique. ram Print version: Schneider, Rolf, 1940- Convex bodies 0521352207 (DLC) 92011481 (OCoLC)25629815 Encyclopedia of mathematics and its applications ; v. 44. http://id.loc.gov/authorities/names/n42010632 FWS01 ZDB-4-EBA FWS_PDA_EBA https://search.ebscohost.com/login.aspx?direct=true&scope=site&db=nlebk&AN=569310 Volltext |
| spellingShingle | Schneider, Rolf, 1940- Convex bodies : the Brunn-Minkowski theory / Encyclopedia of mathematics and its applications ; Cover; Half-title; Title; Copyright; Contents; Preface; Conventions and notation; 1 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 The support function; 1.8 The Hausdorff metric; 2 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 Generic boundary structure; 3 Minkowski addition; 3.1 Minkowski addition and subtraction; 3.2 Summands and decomposition 3.3 Approximation and addition3.4 Additive maps; 3.5 Zonoids and other classes of convex bodies; 4 Curvature measures and quermassintegrals; 4.1 Local parallel sets; 4.2 Curvature measures and area measures; 4.3 The area measure of order one; 4.4 Additive extension; 4.5 Integral-geometric formulae; 4.6 Local behaviour of curvature measures; 5 Mixed volumes and related concepts; 5.1 Mixed volumes and mixed area measures; 5.2 Extensions of mixed volumes; 5.3 Special formulae for mixed volumes and quermassintegrals; 5.4 Moment vectors and curvature centroids; 6 Inequalities for mixed volumes 6.1 The Brunn-Minkowski theorem6.2 The Minkowski and isoperimetric inequalities; 6.3 The Aleksandrov-Fenchel inequality; 6.4 Consequences and improvements; 6.5 Generalized parallel bodies; 6.6 Equality cases and stability; 6.7 Linear inequalities; 6.8 Analogous notions and inequalities; 7 Selected applications; 7.1 Minkowski's existence theorem; 7.2 Uniqueness theorems for area measures; 7.3 The difference-body inequality; 7.4 Affinely associated bodies; Appendix Spherical harmonics; References; List of symbols; Author index; Subject index Convex bodies. http://id.loc.gov/authorities/subjects/sh85031726 Corps convexes. MATHEMATICS Geometry General. bisacsh Convex bodies fast Konvexer Körper gnd http://d-nb.info/gnd/4165214-9 Corps convexes. ram Géométrie analytique. ram |
| subject_GND | http://id.loc.gov/authorities/subjects/sh85031726 http://d-nb.info/gnd/4165214-9 |
| 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 | Convex bodies. http://id.loc.gov/authorities/subjects/sh85031726 Corps convexes. MATHEMATICS Geometry General. bisacsh Convex bodies fast Konvexer Körper gnd http://d-nb.info/gnd/4165214-9 Corps convexes. ram Géométrie analytique. ram |
| topic_facet | Convex bodies. Corps convexes. MATHEMATICS Geometry General. Convex bodies Konvexer Körper Géométrie analytique. |
| url | https://search.ebscohost.com/login.aspx?direct=true&scope=site&db=nlebk&AN=569310 |
| work_keys_str_mv | AT schneiderrolf convexbodiesthebrunnminkowskitheory |