Locality of the mean curvature of rectifiable varifolds
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Bibliographic record
Abstract
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 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 multiplicities on their intersection). We also discuss a couple of applications in elasticity and computer vision.
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| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.000 | 0.000 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.000 | 0.001 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.000 | 0.000 |
| Open science | 0.000 | 0.000 |
| Research integrity | 0.000 | 0.000 |
| Insufficient payload (model declined to judge) | 0.000 | 0.000 |
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