Width of convex bodies in spaces of constant curvature

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

doi:10.1007/s00229-008-0171-1

Width of convex bodies in spaces of constant curvature

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

Departament de Matemàtiques

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Resum

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.

Idioma original	Anglès
Pàgines (de-a)	115-134
Revista	Manuscripta Mathematica
Volum	126
DOIs	https://doi.org/10.1007/s00229-008-0171-1
Estat de la publicació	Publicada - 1 de maig 2008

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10.1007/s00229-008-0171-1

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https://www.scopus.com/pages/publications/42149164954

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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.",

author = "E. Gallego and A. Revent{\'o}s and G. Solanes and E. Teufel",

year = "2008",

month = may,

day = "1",

doi = "10.1007/s00229-008-0171-1",

language = "English",

volume = "126",

pages = "115--134",

journal = "Manuscripta Mathematica",

issn = "0025-2611",

publisher = "Springer New York",

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TY - JOUR

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.

UR - https://www.scopus.com/pages/publications/42149164954

U2 - 10.1007/s00229-008-0171-1

DO - 10.1007/s00229-008-0171-1

M3 - Article

SN - 0025-2611

VL - 126

SP - 115

EP - 134

JO - Manuscripta Mathematica

JF - Manuscripta Mathematica

ER -

Width of convex bodies in spaces of constant curvature

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