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Sharp boundedness and regularizing effects of the integral Menger curvature for submanifolds
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Blatt, Simon and Kolasiński, Sławomir. (2012) Sharp boundedness and regularizing effects of the integral Menger curvature for submanifolds. Advances in Mathematics, Vol.230 (No.3). pp. 839-852. ISSN 0001-8708
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Official URL: http://dx.doi.org/10.1016/j.aim.2012.03.007
Abstract
We show that embedded and compact C 1 manifolds have finite integral Menger curvature if and only if they are locally graphs of functions belonging to certain Sobolev-Slobodeckij spaces. Furthermore, we prove that for some intermediate energies of integral Menger type a similar characterization of objects with finite energy can be given. © 2012 Elsevier Ltd.
| Item Type: | Journal Article |
|---|---|
| Subjects: | Q Science > QA Mathematics |
| Divisions: | Faculty of Science > Mathematics |
| Journal or Publication Title: | Advances in Mathematics |
| Publisher: | Academic Press |
| ISSN: | 0001-8708 |
| Date: | 20 June 2012 |
| Volume: | Vol.230 |
| Number: | No.3 |
| Page Range: | pp. 839-852 |
| Identification Number: | 10.1016/j.aim.2012.03.007 |
| Status: | Peer Reviewed |
| Publication Status: | Published |
| Access rights to Published version: | Restricted or Subscription Access |
| URI: | http://wrap.warwick.ac.uk/id/eprint/49252 |
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