Locality of the mean curvature of rectifiable varifolds
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Gian Paolo Leonardi
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.
© de Gruyter 2009
Articles in the same Issue
- Boundary regularity for polyharmonic maps in the critical dimension
- Locality of the mean curvature of rectifiable varifolds
- Semicontinuity and relaxation of L∞-functionals
- Weak solutions of a biharmonic map heat flow
- p-harmonic energy of deformations between punctured balls
Articles in the same Issue
- Boundary regularity for polyharmonic maps in the critical dimension
- Locality of the mean curvature of rectifiable varifolds
- Semicontinuity and relaxation of L∞-functionals
- Weak solutions of a biharmonic map heat flow
- p-harmonic energy of deformations between punctured balls
