6533b862fe1ef96bd12c6df4

RESEARCH PRODUCT

A new rotational integral formula for intrinsic volumes in space forms

Luis M. Cruz-oriveJ. J. Nuòo-ballesterosXimo Gual-arnau

subject

TransversalityPlane (geometry)Space formApplied MathematicsStereologyMathematical analysisTransversalitySpace formFixed pointSubmanifoldSpace (mathematics)Integral geometryIntersectionMathematics::Metric GeometrySupport setIntegral geometryIntrinsic volumeRotational integralMathematics

description

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. © 2009 Elsevier Inc. All rights reserved.

yearjournalcountryeditionlanguage
2010-03-01
10.1016/j.aam.2009.09.003