Width of convex bodies in spaces of constant curvature

E. Gallego; A. Reventós; G. Solanes; E. Teufel

doi:https://doi.org/10.1007/s00229-008-0171-1

Width of convex bodies in spaces of constant curvature

E. Gallego, A. Reventós, G. Solanes, E. Teufel

Department of Mathematics

Research output: Contribution to journal › Article › Research › peer-review

5 Citations (Scopus)

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 language	English
Pages (from-to)	115-134
Journal	Manuscripta Mathematica
Volume	126
DOIs	https://doi.org/10.1007/s00229-008-0171-1
Publication status	Published - 1 May 2008

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title = "Width of convex bodies in spaces of constant curvature",

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. {\textcopyright} 2008 Springer-Verlag.",

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T1 - Width of convex bodies in spaces of constant curvature

AU - Gallego, E.

AU - Reventós, A.

AU - Solanes, G.

AU - Teufel, E.

PY - 2008/5/1

Y1 - 2008/5/1

N2 - 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.

AB - 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.

U2 - https://doi.org/10.1007/s00229-008-0171-1

DO - https://doi.org/10.1007/s00229-008-0171-1

M3 - Article

VL - 126

SP - 115

EP - 134

JO - Manuscripta Mathematica

JF - Manuscripta Mathematica

SN - 0025-2611

ER -

Width of convex bodies in spaces of constant curvature

Abstract

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