Información General

• Autores: Vladimir Boltyanski, Horst Martini, Petru S. Soltan
• Editores: Berlin : Springer-Verlag, cop. 1997
• Año de publicación: 1997
• País: Alemania
• Idioma: inglés
• ISBN: 3-540-61341-2
• Texto completo no disponible (Saber más ...)

Resumen

• 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 (generally unsolved) problems from the combinatorial geometry of convex bodies: 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.

Otros catálogos

• Red de Bibliotecas Universitarias (REBIUN)

Índice

• I Convexity
  §1 Convex sets
  §2 Faces and supporting hyperplanes
  §3 Polarity
  §4 Direct sum decompositions
  §5 The lower semicontinuity of the operator "exp"
  §6 Convex cones
  §7 The Farkas Lemma and its generalization
  §8 Separable Systems of convex cones
  II d-Convexity in normed spaces
  §9 The definition of d-convex sets
  §10 Support properties of d-convex sets
  §11 Properties of d-convex flats
  §12 The join of normed spaces
  §13 Separability of d-convex sets
  §14 The Helly dimension of a set family
  §15 d-Star-shaped sets
  II H-convexity
  §16 The functional md for vector systems
  §17 TheE-displacement Theorem
  §18 Lower semicontinuity of the functional md
  §19 The definition of H-convex-sets
  §20 Upper semicontinuity of H-convex hull
  §21 Supporting cones of H-convex bodies
  §22 The Helly Theorem for H-convex sets
  §23 Some applications of H-convexity
  §24 Some remarks on connection between d-convexity and H-convexity
  IV The Szökefalvi-Nagy Problem
  §25 The Theorem of Szökefalvi-Nagy and its generalization
  §26 Description of vector systems with md H=2 that are not one-sided
  §27 The 2-systems without particular vectors
  §28 The 2-system wiht particular vectors
  §29 The compact, convex bodies with md M=2
  §30 Centrally symmetric bodies
  V Borsuk's partition problem
  §31 Formulation of the problem and a survey of results
  §32 Bodies of constant width in Euclidean and normed spaces
  §33 Borsuk's problem in normed spaces
  VI Homothetic covering and illumination
  §34 The main problem and a survey of results
  §35 The hypothesis of Gohberg-Markus-Hadwiger
  §36 The infinite values of the functionals b, b', c, c'
  §37 Inner illumination of convex bodies
  §38 Estimates for the value of the functional p(K)
  VII Cominatorial geometry of belt bodies
  §39 The integral representation of zonoids
  §40 Belt vectors of a compact, convex body
  §41 Definition of belt bodies
  §42 Solution of the illuminations problem for belt bodies
  §43 Solution of the Szökefalvi-Nagy problem for belt bodies
  §44 Minumal fixing systems
  VIII Some research problems
  Bibliography
  Author Index
  Subject Index
  List of Symbols