Excursions into combinatorial geometry
By: Vladimir Boltyanski,Horst Martini,Petru S. Soltan.
Contributors: Martini, Horst, 1954-; Soltan, Petr Semenovich.
Series: Universitext; Universitext
Publisher: Springer
Published: 1997
Place of publication: New York; London
Language: eng
Number of pages: 418
Subjects: Combinatorial geometry.; Convex bodies.
Description: The book deals with the combinatorial geometry of convex bodies in finite-dimensional spaces. A general introduction to geometric convexity is followed by the investigation of d-convexity and H-convexity, and by various applications. Recent research is discussed, for example the three problems from the combinatorial geometry of convex bodies (unsolved in the general case): the Szoekefalvi-Nagy problem, the Borsuk problem, the Hadwiger covering problem.

These and related questions are then applied to a new class of convex bodies which is a natural generalization of the class of zonoids: the class of belt bodies. Finally open research problems are discussed. Each section is supplemented by a wide range of exercises and the geometric approach to many topics is illustrated with the help of more than 250 figures.
Notes: Includes bibliographical references (p. [393]-410) and indexes.