The Cauchy Problem for Harmonic Maps on Minkowski Space

Jalal Shatah
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Jalal Shatah: Courant Institute of Mathematical Sciences

A chapter in Proceedings of the International Congress of Mathematicians, 1995, pp 1126-1132 from Springer

Abstract: 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.

Date: 1995
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DOI: 10.1007/978-3-0348-9078-6_105

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