Width of convex bodies in spaces of constant curvature

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Abstract

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. © 2008 Springer-Verlag.
Original languageEnglish
Pages (from-to)115-134
JournalManuscripta Mathematica
Volume126
DOIs
Publication statusPublished - 1 May 2008

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