Locality of the mean curvature of rectifiable varifolds

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