Selected Topics in Convex Geometry

• Main Author: Moszyńska, Maria (Author)
• Corporate Author: SpringerLink (Online service)
• Format: Electronic eBook
• Language: English
• Published: Boston, MA : Birkhäuser Boston, 2006.
• Subjects: Mathematics.; Matrix theory.; Algebra.; Mathematical analysis.; Analysis (Mathematics).; Measure theory.; Applied mathematics.; Engineering mathematics.; Convex geometry.; Discrete geometry.; Topology.; Convex and Discrete Geometry.; Applications of Mathematics.; Analysis.; Measure and Integration.; Linear and Multilinear Algebras, Matrix Theory.

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 biblio...

Table of Contents:

• 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.