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Absolute curvatures in integral geometry

Published online by Cambridge University Press:  24 October 2008

Adrian J. Baddeley
Adrian J. Baddeley
Affiliation:
Trinity College, Cambridge
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Extract

Surface integrals of curvature arise naturally in integral geometry and geometrical probability, most often in connection with the Quermassintegrale or cross-section integrals of convex bodies. They enjoy many desirable properties, such as the ability to be determined by summing or averaging over lower-dimensional sections or projections. In fact the Quermassintegrale are the only functionals of convex bodies to meet certain, quite reasonable, requirements. The conclusion has often been drawn, especially in practical applications, that the Quermassintegrale and their associated curvature integrals have a canonical status to the exclusion of all other quantities.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 88 , Issue 1 , July 1980 , pp. 45 - 58
Copyright
Copyright © Cambridge Philosophical Society 1980

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