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

作者：Gual Arnau Ximo^*; Cruz Orive Luis M

来源：Applications of Mathematics, 2016, 61(4): 489-501.

DOI：10.1007/s10492-016-0143-9

• critical point
• height function
• submanifold in space forms
• invariator principle
• local stereology
• rotational formulae
• 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.

• 出版日期2016-8