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The Cauchy Problem for Harmonic Maps on Minkowski Space

In: Proceedings of the International Congress of Mathematicians

Author

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  • Jalal Shatah

    (Courant Institute of Mathematical Sciences)

Abstract

In this article we shall be reporting on recent progress in the study of harmonic maps from Minkowski space (M, ŋ) into a Riemannian manifold (N, g). These maps (also called wave maps or sigma models) are solutions to the wave equation with partial derivatives replaced by covariant derivatives. These equations are naturally nonlinear because the image lives on a manifold instead of a vector space, as is the case for the linear wave equation. A useful way to describe the problem would be when the target manifold N is a hypersurface in ℝk+1.

Suggested Citation

  • Jalal Shatah, 1995. "The Cauchy Problem for Harmonic Maps on Minkowski Space," Springer Books, in: S. D. Chatterji (ed.), Proceedings of the International Congress of Mathematicians, pages 1126-1132, Springer.
    • Handle: RePEc:spr:sprchp:978-3-0348-9078-6_105
    DOI: 10.1007/978-3-0348-9078-6_105
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