Abstract
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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Cordially dedicated to Professor Vratislav Horálek on his 90th birthday, and to the memory of Professor Ivan Saxl
Work was supported by the UJI project P11B2012-24 and the PROMETEOII/2014/062 project.
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Gual-Arnau, X., Cruz-Orive, L.M. New rotational integrals in space forms, with an application to surface area estimation. Appl Math 61, 489–501 (2016). https://doi.org/10.1007/s10492-016-0143-9
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DOI: https://doi.org/10.1007/s10492-016-0143-9
Keywords
- critical point
- height function
- submanifold in space forms
- invariator principle
- local stereology
- rotational formulae
- surface area estimation