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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. doi:10.1016/j.aim.2012.03.007 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 | ||||
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Subjects: | Q Science > QA Mathematics | ||||
Divisions: | Faculty of Science, Engineering and Medicine > Science > Mathematics | ||||
Journal or Publication Title: | Advances in Mathematics | ||||
Publisher: | Academic Press | ||||
ISSN: | 0001-8708 | ||||
Official Date: | 20 June 2012 | ||||
Dates: |
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Volume: | Vol.230 | ||||
Number: | No.3 | ||||
Page Range: | pp. 839-852 | ||||
DOI: | 10.1016/j.aim.2012.03.007 | ||||
Status: | Peer Reviewed | ||||
Publication Status: | Published | ||||
Access rights to Published version: | Restricted or Subscription Access |
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