Width of convex bodies in spaces of constant curvature

We consider the measure of points, the measure of lines and the measure of planes intersecting a given convex body K in a space form. We obtain some integral formulas involving the width of K and the curvature of its boundary ∂ K . Also we study the special case of constant width. Moreover we obtain...

Full description

Saved in:
Bibliographic Details
Published inManuscripta mathematica Vol. 126; no. 1; pp. 115 - 134
Main Authors Gallego, E., Reventós, A., Solanes, G., Teufel, E.
Format Journal Article
LanguageEnglish
Published Berlin/Heidelberg Springer-Verlag 01.05.2008
Subjects
Algebraic Geometry
Calculus of Variations and Optimal Control; Optimization
Geometry
Lie Groups
Mathematics
Mathematics and Statistics
Number Theory
Topological Groups
Convex Body
Hyperbolic Space
Fundamental Form
Constant Curvature
Constant Width
Online AccessGet full text

Cover

More Information
Summary:We consider the measure of points, the measure of lines and the measure of planes intersecting a given convex body K in a space form. We obtain some integral formulas involving the width of K and the curvature of its boundary ∂ K . Also we study the special case of constant width. Moreover we obtain a generalisation of the Heintze–Karcher inequality to space forms.
ISSN:0025-2611
1432-1785
DOI:10.1007/s00229-008-0171-1