Selected Topics in Convex Geometry

2006
ISBN: 978-0-8176-4396-6
Verlag: Birkhäuser Boston

Buch, Englisch, 226 Seiten, Book w. online files / update, Format (B × H): 155 mm x 235 mm, Gewicht: 382 g

Examines in detail those topics in convex geometry that are concerned with Euclidean space

Enriched by numerous examples, illustrations, and exercises, with a good bibliography and index

Requires only a basic knowledge of geometry, linear algebra, analysis, topology, and measure theory

Can be used for graduates courses or seminars in convex geometry, geometric and convex combinatorics, and convex analysis and optimization

Zielgruppe

Research

Autoren/Hrsg.

Moszynska, Maria

Fachgebiete

• Mathematik | Informatik Mathematik Algebra Homologische Algebra
• Mathematik | Informatik Mathematik Algebra Lineare und multilineare Algebra, Matrizentheorie
• Mathematik | Informatik Mathematik Topologie Mengentheoretische Topologie
• Mathematik | Informatik Mathematik Mathematische Analysis Elementare Analysis und Allgemeine Begriffe
• Mathematik | Informatik Mathematik Geometrie Algebraische Geometrie
• Mathematik | Informatik Mathematik Mathematische Analysis Integralrechnungen- und -gleichungen
• Mathematik | Informatik Mathematik Mathematische Analysis Reelle Analysis
• Mathematik | Informatik Mathematik Numerik und Wissenschaftliches Rechnen Angewandte Mathematik, Mathematische Modelle
• Mathematik | Informatik Mathematik Numerik und Wissenschaftliches Rechnen Computeranwendungen in der Mathematik

Inhaltsverzeichnis

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.