The aim of this paper is to investigate whether, given two rectifiable k-varifolds in Rn with locally bounded first variations and integer-valued multiplicities, their mean curvatures coincide Hk-almost everywhere on the intersection of the supports of their weight measures. This so-called locality property, which is well known for classical C2 surfaces, is far from being obvious in the context of varifolds. We prove that the locality property holds true for integral 1-varifolds, while for k-varifolds, k > 1, we are able to prove that it is verified under some additional assumptions (local inclusion of the supports and locally constant multiplicities on their intersection). We also discuss a couple of applications in elasticity and computer vision.

Locality of the mean curvature of rectifiable varifolds / Leonardi, G. P.; Masnou, S.. - In: ADVANCES IN CALCULUS OF VARIATIONS. - ISSN 1864-8258. - STAMPA. - 2:1(2009), pp. 17-42. [10.1515/ACV.2009.002]

Locality of the mean curvature of rectifiable varifolds

Leonardi G.P.;
2009-01-01

Abstract

The aim of this paper is to investigate whether, given two rectifiable k-varifolds in Rn with locally bounded first variations and integer-valued multiplicities, their mean curvatures coincide Hk-almost everywhere on the intersection of the supports of their weight measures. This so-called locality property, which is well known for classical C2 surfaces, is far from being obvious in the context of varifolds. We prove that the locality property holds true for integral 1-varifolds, while for k-varifolds, k > 1, we are able to prove that it is verified under some additional assumptions (local inclusion of the supports and locally constant multiplicities on their intersection). We also discuss a couple of applications in elasticity and computer vision.
2009
1
Leonardi, G. P.; Masnou, S.
Locality of the mean curvature of rectifiable varifolds / Leonardi, G. P.; Masnou, S.. - In: ADVANCES IN CALCULUS OF VARIATIONS. - ISSN 1864-8258. - STAMPA. - 2:1(2009), pp. 17-42. [10.1515/ACV.2009.002]
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11572/229172
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