Speight, JM (2015) The adiabatic limit of wave-map flow on the two-torus. Transactions of the American Mathematical Society, 367 (12). pp. 8997-9026. ISSN 0002-9947
Abstract
The S2 valued wave map flow on a Lorentzian domain R × Σ, where Σ is any flat two-torus, is studied. The Cauchy problem with initial data tangent to the moduli space of holomorphic maps Σ → S2 is onsidered, in the limit of small initial velocity. It is proved that wave maps, in this limit, converge in a precise sense to geodesics in the moduli space of holomorphic maps, with respect to the L2 metric. This establishes, in a rigorous setting, a long-standing informal conjecture of Ward.
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Copyright, Publisher and Additional Information: | © 2015 American Mathematical Society. First published in Transactions of the American Mathematical Society in 367(12), 2015, published by the American Mathematical Society. | ||||||
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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) | ||||||
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Depositing User: | Symplectic Publications | ||||||
Date Deposited: | 08 Oct 2015 12:26 | ||||||
Last Modified: | 27 Oct 2016 19:04 | ||||||
Published Version: | http://dx.doi.org/10.1090/tran/6538 | ||||||
Status: | Published | ||||||
Publisher: | American Mathematical Society | ||||||
Identification Number: | https://doi.org/10.1090/tran/6538 |