A new rotational integral formula for intrinsic volumes in space forms

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 func...

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Veröffentlicht in:	Advances in applied mathematics 2010-03, Vol.44 (3), p.298-308
Hauptverfasser:	Gual-Arnau, X., Cruz-Orive, L.M., Nuño-Ballesteros, J.J.
Format:	Artikel
Sprache:	eng
Schlagworte:	Differential geometry Exact sciences and technology General mathematics General, history and biography Geometry Global analysis, analysis on manifolds Integral geometry Integrals Intersections Intrinsic volume Mathematical analysis Mathematics Numerical analysis Numerical analysis. Scientific computation Planes Rotational Rotational integral Sciences and techniques of general use Space form Stereology Support set Topology. Manifolds and cell complexes. Global analysis and analysis on manifolds Transversality
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Beschreibung
Zusammenfassung:	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.
ISSN:	0196-8858 1090-2074
DOI:	10.1016/j.aam.2009.09.003