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The adiabatic limit of wave map flow on a two torus
- Publication Year :
- 2012
-
Abstract
- The two-sphere valued wave map flow on a Lorentzian domain R x Sigma, where Sigma is any flat two-torus, is studied. The Cauchy problem with initial data tangent to the moduli space of holomorphic maps Sigma -> S^2 is considered, 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 L^2 metric. This establishes, in a rigorous setting, a long-standing informal conjecture of Ward.<br />Comment: 33 pages. Version accepted for publication. Includes updated discussion of the literature on blow-up
Details
- Database :
- arXiv
- Publication Type :
- Report
- Accession number :
- edsarx.1207.4367
- Document Type :
- Working Paper