Strange phenomena in convex and discrete geometry:
This book presents some of the most famous problems of convex and discrete geometry - such as Borsuk's problem (is it possible to partition any bounded set in an n-dimensional Euclidean space into n+1 subsets, each of which is strictly smaller in diameter than the full set?) and the finite sphe...
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
New York [u.a.]
Springer
1996
|
| Series: | Universitext
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| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Summary: | This book presents some of the most famous problems of convex and discrete geometry - such as Borsuk's problem (is it possible to partition any bounded set in an n-dimensional Euclidean space into n+1 subsets, each of which is strictly smaller in diameter than the full set?) and the finite sphere-packing problem (how can one arrange m nonoverlapping congruent spheres in an n-dimensional Euclidean space to minimize the volume or surface area of their convex hull?) - as well as their (at times astonishing) answers. Though covering some of the most recent developments in the field, the book is self-contained, and can be understood by any trained mathematician. |
| Physical Description: | X, 158 S. graph. Darst. |
| ISBN: | 0387947345 |
Staff View
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| 520 | 3 | |a This book presents some of the most famous problems of convex and discrete geometry - such as Borsuk's problem (is it possible to partition any bounded set in an n-dimensional Euclidean space into n+1 subsets, each of which is strictly smaller in diameter than the full set?) and the finite sphere-packing problem (how can one arrange m nonoverlapping congruent spheres in an n-dimensional Euclidean space to minimize the volume or surface area of their convex hull?) - as well as their (at times astonishing) answers. Though covering some of the most recent developments in the field, the book is self-contained, and can be understood by any trained mathematician. | |
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Record in the Search Index
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|---|---|
| adam_text | Contents
Preface v
Basic Notation vii
1 Borsuk s Problem 1
§1 Introduction 1
§2 The Perkal Eggleston Theorem 2
§3 Some Remarks 7
§4 Larman s Problem 8
§5 The Kahn Kalai Phenomenon 9
2 Finite Packing Problems 15
§1 Introduction 15
§2 Supporting Functions, Area Functions, Minkowski Sums,
Mixed Volumes, and Quermassintegrals 16
§3 The Optimal Finite Packings Regarding Quermassintegrals 18
§4 The L. Fejes Toth Betke Henk Wills Phenomenon 23
§5 Some Historical Remarks 34
3 The Venkov McMullen Theorem
and Stein s Phenomenon 37
§1 Introduction 37
§2 Convex Bodies and Their Area Functions 37
§3 The Venkov McMullen Theorem 43
x Contents
§4 Stein s Phenomenon 50
§5 Some Remarks 53
4 Local Packing Phenomena 55
§1 Introduction 55
§2 A Phenomenon Concerning Blocking Numbers
and Kissing Numbers 57
§3 A Basic Approximation Result 62
§4 Minkowski s Criteria for Packing Lattices
and the Densest Packing Lattices 63
§5 A Phenomenon Concerning Kissing Numbers
and Packing Densities 70
§6 Remarks and Open Problems 81
5 Category Phenomena 83
§1 Introduction 83
§2 Gruber s Phenomenon 84
§3 The Aleksandrov Busemann Feller Theorem 85
§4 A Theorem of Zamfirescu 90
§5 The Schneider Zamfirescu Phenomenon 91
§6 Some Remarks 98
6 The Busemann Petty Problem 99
§1 Introduction 99
§2 Steiner Symmetrization 100
§3 A Theorem of Busemann 101
§4 The Larman Rogers Phenomenon 108
§5 Schneider s Phenomenon 113
§6 Some Historical Remarks 121
7 Dvoretzky s Theorem 123
§1 Introduction 123
§2 Preliminaries 123
§3 Technical Introduction 126
§4 A Lemma of Dvoretzky and Rogers 128
§5 An Estimate for av{Av) 130
§6 /3 nets and e spheres 134
§7 A Proof of Dvoretzky s Theorem 136
§8 An Upper Bound for M(n, e) 137
§9 Some Historical Remarks 141
Bibliography 143
Index 155
|
| any_adam_object | 1 |
| author | Zong, Chuanming |
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| discipline | Mathematik |
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| id | DE-604.BV010937779 |
| illustrated | Illustrated |
| indexdate | 2024-07-09T18:01:23Z |
| institution | BVB |
| isbn | 0387947345 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-007316543 |
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| physical | X, 158 S. graph. Darst. |
| publishDate | 1996 |
| publishDateSearch | 1996 |
| publishDateSort | 1996 |
| publisher | Springer |
| record_format | marc |
| series2 | Universitext |
| spelling | Zong, Chuanming Verfasser aut Strange phenomena in convex and discrete geometry Chuanming Zong New York [u.a.] Springer 1996 X, 158 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Universitext This book presents some of the most famous problems of convex and discrete geometry - such as Borsuk's problem (is it possible to partition any bounded set in an n-dimensional Euclidean space into n+1 subsets, each of which is strictly smaller in diameter than the full set?) and the finite sphere-packing problem (how can one arrange m nonoverlapping congruent spheres in an n-dimensional Euclidean space to minimize the volume or surface area of their convex hull?) - as well as their (at times astonishing) answers. Though covering some of the most recent developments in the field, the book is self-contained, and can be understood by any trained mathematician. Convex geometry Discrete geometry Diskrete Geometrie (DE-588)4130271-0 gnd rswk-swf Konvexe Geometrie (DE-588)4407260-0 gnd rswk-swf Konvexe Geometrie (DE-588)4407260-0 s DE-604 Diskrete Geometrie (DE-588)4130271-0 s HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=007316543&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Zong, Chuanming Strange phenomena in convex and discrete geometry Convex geometry Discrete geometry Diskrete Geometrie (DE-588)4130271-0 gnd Konvexe Geometrie (DE-588)4407260-0 gnd |
| subject_GND | (DE-588)4130271-0 (DE-588)4407260-0 |
| title | Strange phenomena in convex and discrete geometry |
| title_auth | Strange phenomena in convex and discrete geometry |
| title_exact_search | Strange phenomena in convex and discrete geometry |
| title_full | Strange phenomena in convex and discrete geometry Chuanming Zong |
| title_fullStr | Strange phenomena in convex and discrete geometry Chuanming Zong |
| title_full_unstemmed | Strange phenomena in convex and discrete geometry Chuanming Zong |
| title_short | Strange phenomena in convex and discrete geometry |
| title_sort | strange phenomena in convex and discrete geometry |
| topic | Convex geometry Discrete geometry Diskrete Geometrie (DE-588)4130271-0 gnd Konvexe Geometrie (DE-588)4407260-0 gnd |
| topic_facet | Convex geometry Discrete geometry Diskrete Geometrie Konvexe Geometrie |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=007316543&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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