Geodesic
New rotational integrals in space forms, with an application to surface area estimation
Applications of Mathematics, Tome 61 (2016) no. 4, pp. 489-501

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A surface area estimator for three-dimensional convex sets, based on the invariator principle of local stereology, has recently motivated its generalization by means of new rotational Crofton-type formulae using Morse theory. We follow a different route to obtain related formulae which are more manageable and valid for submanifolds in constant curvature spaces. As an application, we obtain a simplified version of the mentioned surface area estimator for non-convex sets of smooth boundary.
DOI : 10.1007/s10492-016-0143-9
Classification : 53C65
Keywords: critical point; height function; submanifold in space forms; invariator principle; local stereology; rotational formulae; surface area estimation 
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Gual-Arnau, Ximo; Cruz-Orive, Luis M. New rotational integrals in space forms, with an application to surface area estimation. Applications of Mathematics, Tome 61 (2016) no. 4, pp. 489-501. doi: 10.1007/s10492-016-0143-9

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