A new rotational integral formula for intrinsic volumes in space forms

X Gual-Arnau,L.M Cruz-Orive,J.J Nuño-Ballesteros

doi:10.1016/j.aam.2009.09.003

A new rotational integral formula for intrinsic volumes in space forms

X Gual-Arnau, L.M Cruz-Orive + Show 1 more

https://doi.org/10.1016/j.aam.2009.09.003

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Journal: Advances in Applied Mathematics	Publication Date: Oct 30, 2009
Citations: 23	License type: elsevier-specific: oa user license

Affiliation: Jaume I University, University of Valencia

#Space Form #Crofton's Formula + Show 8 more

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Abstract

A new rotational version of Crofton's formula is derived for the intrinsic volumes of a domain Y in a space form. More precisely, a functional is defined on the intersection between Y and a totally geodesic submanifold (plane) through a fixed point, such that the rotational average of this functional is equal to the intrinsic volumes of Y. Particular cases of interest in stereology are considered for the Euclidean case.

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