### Locality of the mean curvature of rectifiable varifolds

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**Abstract:** The aim of this paper is to investigate whether, given two rectifiable *k*-varifolds in R^{n} with locally bounded first variations and integer-valued multiplicities, their generalized mean curvatures coincide *H*^{k} -almost everywhere on the intersection of the supports of their weight measures. This so-called* locality property*, which is well-known for classical *C*^{2} 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 multiplicity on their intersection). We also discuss a couple of applications in elasticity and computer vision.

**Mots Clés:** *Varifolds; Mean curvature; Semicontinuity; Willmore energy; Image reconstruction*

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