The field of convex geometry has become a fertile subject of mathematical activity in the past few decades. This exposition, examining in detail those topics in convex geometry that are concerned with Euclidean space, is enriched by numerous examples, illustrations, and exercises, with a good bibliography and index. It requires of the reader only a basic knowledge of geometry, linear algebra, analysis, topology, and measure theory. The book can be used in the classroom setting for graduates courses or seminars in convex geometry, geometric and convex combinatorics, and convex analysis and optimization. Researchers in pure and applied areas will also benefit from the book.
Rezensionen / Stimmen
From the reviews:
"This book is the translation and revision of the original Polish 2001 edition. Its focus is on studying convexity for its own sake rather than on applications of convexity . . The readable book contains numerous examples and some exercises. . the book could be used by students for courses or seminars in several geometric fields." (E. Hertel, Mathematical Reviews, Issue 2006 g)
Auflage
Sprache
Verlagsort
Zielgruppe
Für Beruf und Forschung
Research
Illustrationen
30
30 s/w Abbildungen
XVIII, 226 p. 30 illus. With online files/update.
Maße
Höhe: 235 mm
Breite: 155 mm
Dicke: 14 mm
Gewicht
ISBN-13
978-0-8176-4396-6 (9780817643966)
DOI
Schweitzer Klassifikation
I.- Metric Spaces.- Subsets of Euclidean Space.- Basic Properties of Convex Sets.- Transformations of the Space Kn of Compact Convex Sets.- Rounding Theorems.- Convex Polytopes.- Functionals on the Space Kn. The Steiner Theorem.- The Hadwiger Theorems.- Applications of the Hadwiger Theorems.- II.- Curvature and Surface Area Measures.- Sets with positive reach. Convexity ring.- Selectors for Convex Bodies.- Polarity.- III.- Star Sets. Star Bodies.- Intersection Bodies.- Selectors for Star Bodies.