A kinematic formula for the total absolute curvature of intersections

E. Gallego; G. Solanes; E. Teufel; Agusti Reventos Tarrida

doi:https://doi.org/10.1515/ADVGEOM.2010.034

A kinematic formula for the total absolute curvature of intersections

E. Gallego, G. Solanes, E. Teufel, Agusti Reventos Tarrida

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

Abstract

Given two surfaces in three dimensional euclidean space, one fixed and the other moved by rigid motions, we consider the total absolute curvature of the intersection curves. In this paper we investigate the integral of these total absolute curvatures over all motions. Under some geometric conditions we obtain kinematic formulas, and with weaker conditions we get upper and lower bounds. Finally, as applications, we obtain upper bounds for the average number of connected components of the intersections, and we give Hadwiger conditions for a convex domain to be able to contain another one. © 2010 de Gruyter.

Original language	English
Pages (from-to)	709-718
Journal	Advances in Geometry
Volume	10
DOIs	https://doi.org/10.1515/ADVGEOM.2010.034
Publication status	Published - 1 Oct 2010

Keywords

Integral geometry
Kinematic formulas
Total absolute curvature

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title = "A kinematic formula for the total absolute curvature of intersections",

abstract = "Given two surfaces in three dimensional euclidean space, one fixed and the other moved by rigid motions, we consider the total absolute curvature of the intersection curves. In this paper we investigate the integral of these total absolute curvatures over all motions. Under some geometric conditions we obtain kinematic formulas, and with weaker conditions we get upper and lower bounds. Finally, as applications, we obtain upper bounds for the average number of connected components of the intersections, and we give Hadwiger conditions for a convex domain to be able to contain another one. {\textcopyright} 2010 de Gruyter.",

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T1 - A kinematic formula for the total absolute curvature of intersections

AU - Gallego, E.

AU - Solanes, G.

AU - Teufel, E.

AU - Reventos Tarrida, Agusti

PY - 2010/10/1

Y1 - 2010/10/1

N2 - Given two surfaces in three dimensional euclidean space, one fixed and the other moved by rigid motions, we consider the total absolute curvature of the intersection curves. In this paper we investigate the integral of these total absolute curvatures over all motions. Under some geometric conditions we obtain kinematic formulas, and with weaker conditions we get upper and lower bounds. Finally, as applications, we obtain upper bounds for the average number of connected components of the intersections, and we give Hadwiger conditions for a convex domain to be able to contain another one. © 2010 de Gruyter.

AB - Given two surfaces in three dimensional euclidean space, one fixed and the other moved by rigid motions, we consider the total absolute curvature of the intersection curves. In this paper we investigate the integral of these total absolute curvatures over all motions. Under some geometric conditions we obtain kinematic formulas, and with weaker conditions we get upper and lower bounds. Finally, as applications, we obtain upper bounds for the average number of connected components of the intersections, and we give Hadwiger conditions for a convex domain to be able to contain another one. © 2010 de Gruyter.

KW - Integral geometry

KW - Kinematic formulas

KW - Total absolute curvature

U2 - https://doi.org/10.1515/ADVGEOM.2010.034

DO - https://doi.org/10.1515/ADVGEOM.2010.034

M3 - Article

SN - 1615-715X

VL - 10

SP - 709

EP - 718

JO - Advances in Geometry

JF - Advances in Geometry

ER -

A kinematic formula for the total absolute curvature of intersections

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Keywords

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