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On Schrödinger and wave maps. (English) Zbl 1065.35105
Beckner, William (ed.) et al., Harmonic analysis at Mount Holyoke. Proceedings of an AMS-IMS-SIAM joint summer research conference, Mount Holyoke College, South Hadley, MA, USA, June 25–July 5, 2001. Providence, RI: American Mathematical Society (AMS) (ISBN 0-8218-2903-3/pbk). Contemp. Math. 320, 295-322 (2003).
This is a survey article presenting mainly the results of A. R. Nahmod, A. Stefanov and K. Uhlenbeck [Commun. Pure Appl. Math. 56, No. 1, 114–151 (2003; Zbl 1028.58018)] and A. R. Nahmod, A. Stefanov, K. Uhlenbeck [Commun. Anal. Geom. 11, 49–83 (2003)]. The subject are Schrödinger maps and wave maps (which are two different hyperbolic versions of harmonic maps) from Minkowski space into compact Riemannian manifolds. The survey focusses on the results and stresses similarities in the methods used, including methods from harmonic analysis and gauge theory.
MSC:
35J10Schrödinger operator
42B35Function spaces arising in harmonic analysis
58J45Hyperbolic partial differential equations on manifolds