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A general formula for the anisotropic outer Minkowski content of a set

Part of: Manifolds General convexity Classical measure theory

Published online by Cambridge University Press:  03 March 2016

Luca Lussardi  and
Elena Villa
Luca Lussardi
Affiliation:
Dipartimento di Matematica e Fisica ‘N. Tartaglia’, Università Cattolica del Sacro Cuore, via dei Musei 41, 25121 Brescia, Italy (luca.lussardi@unicatt.it)
Elena Villa
Affiliation:
Dipartimento di Matematica ‘F. Enriques’, Università degli Studi di Milano, via C. Saldini 50, 20133 Milano, Italy (elena.villa@unimi.it)
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Abstract

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We generalize to the anisotropic case some classical and recent results on the (n – 1)-Minkowski content of rectifiable sets in ℝn, and on the outer Minkowski content of subsets of ℝn. In particular, a general formula for the anisotropic outer Minkowski content is provided; it applies to a wide class of sets that are stable under finite unions.

Keywords

Minkowski contentouter Minkowski contentanisotropyrectifiability

MSC classification

Primary: 28A75: Length, area, volume, other geometric measure theory 49Q15: Geometric measure and integration theory, integral and normal currents 52A39: Mixed volumes and related topics
Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 146 , Issue 2 , April 2016 , pp. 393 - 413
Copyright
Copyright © Royal Society of Edinburgh 2016