Kokarev, G (2014) Variational aspects of Laplace eigenvalues on Riemannian surfaces. Advances in Mathematics, 258. pp. 191-239. ISSN 0001-8708
Abstract
We study the existence and properties of metrics maximising the first Laplace eigenvalue among conformal metrics of unit volume on Riemannian surfaces. We describe a general approach to this problem and its higher eigenvalue versions via the direct method of calculus of variations. The principal results include the general regularity properties of λk-extremal metrics and the existence of a partially regular λ₁-maximiser.
Metadata
Item Type: | Article |
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Authors/Creators: |
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Copyright, Publisher and Additional Information: | © 2014 Elsevier Inc. This is an author produced version of a paper published in Advances in Mathematics. Uploaded in accordance with the publisher's self-archiving policy. |
Keywords: | Laplace eigenvalues; Conformal spectrum; Extremal metrics; Partial regularity; Isocapacitory inequalities |
Dates: |
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Institution: | The University of Leeds |
Academic Units: | The University of Leeds > Faculty of Engineering & Physical Sciences (Leeds) > School of Mathematics (Leeds) > Pure Mathematics (Leeds) |
Depositing User: | Symplectic Publications |
Date Deposited: | 22 Jun 2016 08:33 |
Last Modified: | 17 Jan 2018 06:08 |
Published Version: | http://dx.doi.org/10.1016/j.aim.2014.03.006 |
Status: | Published |
Publisher: | Elsevier |
Identification Number: | 10.1016/j.aim.2014.03.006 |
Open Archives Initiative ID (OAI ID): | oai:eprints.whiterose.ac.uk:98567 |