New rotational integrals in space forms, with an application to surface area estimation

Ximo Gual-Arnau; Luis M. Cruz-Orive

Applications of Mathematics (2016)

  • Volume: 61, Issue: 4, page 489-501
  • ISSN: 0862-7940

Abstract

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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.

How to cite

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Gual-Arnau, Ximo, and Cruz-Orive, Luis M.. "New rotational integrals in space forms, with an application to surface area estimation." Applications of Mathematics 61.4 (2016): 489-501. <http://eudml.org/doc/283399>.

@article{Gual2016,
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.},
author = {Gual-Arnau, Ximo, Cruz-Orive, Luis M.},
journal = {Applications of Mathematics},
keywords = {critical point; height function; submanifold in space forms; invariator principle; local stereology; rotational formulae; surface area estimation; critical point; height function; submanifold in space forms; invariator principle; local stereology; rotational formulae; surface area estimation},
language = {eng},
number = {4},
pages = {489-501},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {New rotational integrals in space forms, with an application to surface area estimation},
url = {http://eudml.org/doc/283399},
volume = {61},
year = {2016},
}

TY - JOUR
AU - Gual-Arnau, Ximo
AU - Cruz-Orive, Luis M.
TI - New rotational integrals in space forms, with an application to surface area estimation
JO - Applications of Mathematics
PY - 2016
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 61
IS - 4
SP - 489
EP - 501
AB - 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.
LA - eng
KW - critical point; height function; submanifold in space forms; invariator principle; local stereology; rotational formulae; surface area estimation; critical point; height function; submanifold in space forms; invariator principle; local stereology; rotational formulae; surface area estimation
UR - http://eudml.org/doc/283399
ER -

References

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