New rotational integrals in space forms, with an application to surface area estimation
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Título
New rotational integrals in space forms, with an application to surface area estimationFecha de publicación
2016-08Editor
SpringerISSN
0862-7940Cita bibliográfica
GUAL-ARNAU, Ximo; CRUZ-ORIVE, Luis M. New rotational integrals in space forms, with an application to surface area estimation. Applications of Mathematics, 2016, vol. 61, no 4, p. 489-501Tipo de documento
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The original publication is available at www.dml.czVersión
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Resumen
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 ... [+]
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. [-]
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Applications of Mathematics, 2016, vol. 61, no 4Derechos de acceso
© Institute of Mathematics of the Academy of Sciences of the Czech Republic, Praha, Czech Republic 2016
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