Measures of symmetry for convex sets and stability:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Elektronisch E-Book |
| Sprache: | English |
| Veröffentlicht: |
Cham
Springer
[2015]
|
| Schriftenreihe: | Universitext
|
| Schlagworte: | |
| Online-Zugang: | BTU01 FRO01 TUM01 UBM01 UBT01 UBW01 UPA01 Volltext Inhaltsverzeichnis Abstract |
| Beschreibung: | 1 Online Ressource (XII, 278 Seiten, 65 illus., 1 illus. in color) |
| ISBN: | 9783319237336 |
| ISSN: | 0172-5939 |
| DOI: | 10.1007/978-3-319-23733-6 |
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Datensatz im Suchindex
| _version_ | 1804175709149593600 |
|---|---|
| adam_text | MEASURES OF SYMMETRY FOR CONVEX SETS AND STABILITY
/ TOTH, GABOR
: 2015
TABLE OF CONTENTS / INHALTSVERZEICHNIS
FIRST THINGS FIRST ON CONVEX SETS
AFFINE DIAMETERS AND THE CRITICAL SET
MEASURES OF STABILITY AND SYMMETRY
MEAN MINKOWSKI MEASURES
DIESES SCHRIFTSTUECK WURDE MASCHINELL ERZEUGT.
MEASURES OF SYMMETRY FOR CONVEX SETS AND STABILITY
/ TOTH, GABOR
: 2015
ABSTRACT / INHALTSTEXT
THIS TEXTBOOK TREATS TWO IMPORTANT AND RELATED MATTERS IN CONVEX
GEOMETRY: THE QUANTIFICATION OF SYMMETRY OF A CONVEX SET—MEASURES OF
SYMMETRY—AND THE DEGREE TO WHICH CONVEX SETS THAT NEARLY MINIMIZE SUCH
MEASURES OF SYMMETRY ARE THEMSELVES NEARLY SYMMETRIC—THE PHENOMENON OF
STABILITY. BY GATHERING THE SUBJECT’S CORE IDEAS AND HIGHLIGHTS AROUND
GRUENBAUM’S GENERAL NOTION OF MEASURE OF SYMMETRY, IT PAINTS A
COHERENT PICTURE OF THE SUBJECT, AND GUIDES THE READER FROM THE BASICS
TO THE STATE-OF-THE-ART. THE EXPOSITION TAKES VARIOUS PATHS TO RESULTS
IN ORDER TO DEVELOP THE READER’S GRASP OF THE UNITY OF IDEAS, WHILE
INTERSPERSED REMARKS ENRICH THE MATERIAL WITH A BEHIND-THE-SCENES VIEW
OF COROLLARIES AND LOGICAL CONNECTIONS, ALTERNATIVE PROOFS, AND ALLIED
RESULTS FROM THE LITERATURE.NUMEROUS ILLUSTRATIONS ELUCIDATE DEFINITIONS
AND KEY CONSTRUCTIONS, AND OVER 70 EXERCISES—WITH HINTS AND REFERENCES
FOR THE MORE DIFFICULT ONES—TEST AND SHARPEN THE READER’S
COMPREHENSION. THE PRESENTATION INCLUDES: A BASIC COURSE COVERING
FOUNDATIONAL NOTIONS IN CONVEX GEOMETRY, THE THREE PILLARS OF THE
COMBINATORIAL THEORY (THE THEOREMS OF CARATHEODORY, RADON, AND HELLY),
CRITICAL SETS AND MINKOWSKI MEASURE, THE MINKOWSKI–RADON INEQUALITY,
AND, TO ILLUSTRATE THE GENERAL THEORY, A STUDY OF CONVEX BODIES OF
CONSTANT WIDTH; TWO PROOFS OF F.JOHN’S ELLIPSOID THEOREM; A TREATMENT
OF THE STABILITY OF MINKOWSKI MEASURE, THE BANACH–MAZUR METRIC, AND
GROEMER’S STABILITY ESTIMATE FOR THE BRUNN–MINKOWSKI INEQUALITY;
IMPORTANT SPECIALIZATIONS OF GRUENBAUM’S ABSTRACT MEASURE OF SYMMETRY,
SUCH AS WINTERNITZ MEASURE, THE ROGERS–SHEPARD VOLUME RATIO, AND
GUO’S LP -MINKOWSKI MEASURE; A CONSTRUCTION BY THE AUTHOR OF A NEW
SEQUENCE OF MEASURES OF SYMMETRY, THE KTH MEAN MINKOWSKI MEASURE; AND
LASTLY, AN INTRIGUING APPLICATION TO THE MODULI SPACE OF CERTAIN
DISTINGUISHED MAPS FROM A RIEMANNIAN HOMOGENEOUS SPACE TO
SPHERES—ILLUSTRATING THE BROAD MATHEMATICAL RELEVANCE OF THE BOOK’S
SUBJECT
DIESES SCHRIFTSTUECK WURDE MASCHINELL ERZEUGT.
|
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| author | Toth, Gabor 1954- |
| author_GND | (DE-588)173585590 |
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| dewey-full | 516.1 |
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| dewey-ones | 516 - Geometry |
| dewey-raw | 516.1 |
| dewey-search | 516.1 |
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| discipline | Mathematik |
| doi_str_mv | 10.1007/978-3-319-23733-6 |
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| indexdate | 2024-07-10T07:20:36Z |
| institution | BVB |
| isbn | 9783319237336 |
| issn | 0172-5939 |
| language | English |
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| spelling | Toth, Gabor 1954- Verfasser (DE-588)173585590 aut Measures of symmetry for convex sets and stability Gabor Toth Cham Springer [2015] © 2015 1 Online Ressource (XII, 278 Seiten, 65 illus., 1 illus. in color) txt rdacontent c rdamedia cr rdacarrier Universitext 0172-5939 Mathematics Convex geometry Discrete geometry Convex and Discrete Geometry Mathematik Konvexe Menge (DE-588)4165212-5 gnd rswk-swf Konvexe Menge (DE-588)4165212-5 s DE-604 Erscheint auch als Druckausgabe 978-3-319-23732-9 https://doi.org/10.1007/978-3-319-23733-6 Verlag Volltext Springer Fremddatenuebernahme application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=028632900&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis Springer Fremddatenuebernahme application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=028632900&sequence=000003&line_number=0002&func_code=DB_RECORDS&service_type=MEDIA Abstract |
| spellingShingle | Toth, Gabor 1954- Measures of symmetry for convex sets and stability Mathematics Convex geometry Discrete geometry Convex and Discrete Geometry Mathematik Konvexe Menge (DE-588)4165212-5 gnd |
| subject_GND | (DE-588)4165212-5 |
| title | Measures of symmetry for convex sets and stability |
| title_auth | Measures of symmetry for convex sets and stability |
| title_exact_search | Measures of symmetry for convex sets and stability |
| title_full | Measures of symmetry for convex sets and stability Gabor Toth |
| title_fullStr | Measures of symmetry for convex sets and stability Gabor Toth |
| title_full_unstemmed | Measures of symmetry for convex sets and stability Gabor Toth |
| title_short | Measures of symmetry for convex sets and stability |
| title_sort | measures of symmetry for convex sets and stability |
| topic | Mathematics Convex geometry Discrete geometry Convex and Discrete Geometry Mathematik Konvexe Menge (DE-588)4165212-5 gnd |
| topic_facet | Mathematics Convex geometry Discrete geometry Convex and Discrete Geometry Mathematik Konvexe Menge |
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