New rotational integrals in space forms, with an application to surface area estimation
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 mana...
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| Veröffentlicht in: | Applications of mathematics (Prague) 2016-08, Vol.61 (4), p.489-501 |
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| container_title | Applications of mathematics (Prague) |
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| creator | Gual-Arnau, Ximo Cruz-Orive, Luis M. |
| description | 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_str_mv | 10.1007/s10492-016-0143-9 |
| format | Article |
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| ispartof | Applications of mathematics (Prague), 2016-08, Vol.61 (4), p.489-501 |
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| source | Free E-Journal (出版社公開部分のみ）; SpringerLink Journals - AutoHoldings |
| subjects | Analysis Applications of Mathematics Classical and Continuum Physics Constants Estimating techniques Estimators Euclidean space Formulas (mathematics) Mathematical analysis Mathematical and Computational Engineering Mathematical and Computational Physics Mathematics Mathematics and Statistics Optimization Smooth boundaries Stereology Studies Surface area Theoretical Topological manifolds |
| title | New rotational integrals in space forms, with an application to surface area estimation |
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