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An improved geometric inequality via vanishing moments, with applications to singular liouville equations
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Bartolucci, Daniele and Malchiodi, Andrea (2013) An improved geometric inequality via vanishing moments, with applications to singular liouville equations. Communications in Mathematical Physics, Volume 322 (Number 2). pp. 415-452. doi:10.1007/s00220-013-1731-0 ISSN 0010-3616.
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Official URL: http://dx.doi.org/10.1007/s00220-013-1731-0
Abstract
We consider a class of singular Liouville equations on compact surfaces motivated by the study of Electroweak and Self-Dual Chern-Simons theories, the Gaussian curvature prescription with conical singularities and Onsager's description of turbulence. We analyse the problem of existence variationally, and show how the angular distribution of the conformal volume near the singularities may lead to improvements in the Moser-Trudinger inequality, and in turn to lower bounds on the Euler-Lagrange functional. We then discuss existence and non-existence results.
Item Type: | Journal Article | ||||
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Divisions: | Faculty of Science, Engineering and Medicine > Science > Mathematics | ||||
Journal or Publication Title: | Communications in Mathematical Physics | ||||
Publisher: | Springer | ||||
ISSN: | 0010-3616 | ||||
Official Date: | 2013 | ||||
Dates: |
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Volume: | Volume 322 | ||||
Number: | Number 2 | ||||
Page Range: | pp. 415-452 | ||||
DOI: | 10.1007/s00220-013-1731-0 | ||||
Status: | Peer Reviewed | ||||
Publication Status: | Published | ||||
Access rights to Published version: | Restricted or Subscription Access |
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