Applications of Mathematics

, Volume 61, Issue 4, pp 489–501 | Cite as

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 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.


critical point height function submanifold in space forms invariator principle local stereology rotational formulae surface area estimation 

MSC 2010



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Copyright information

© Institute of Mathematics of the Academy of Sciences of the Czech Republic, Praha, Czech Republic 2016

Authors and Affiliations

  1. 1.Departament de Matemàtiques-INITUniversitat Jaume ICastelló de la PlanaSpain
  2. 2.Departamento de Matemáticas, Estadística y ComputaciónUniversidad de CantabriaSantanderSpain

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