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MiS Preprint
70/2016
Global existence of the harmonic map heat flow into Lorentzian manifolds
Xiaoli Han, Jürgen Jost, Lei Liu and Liang Zhao
Abstract
We investigate a parabolic-elliptic system for maps from a compact Riemann surface $M$ into a Lorentzian manifold $N\times{\mathbb{R}}$ with a warped product metric. We prove a global existence result of the parabolic-elliptic system by assuming either some geometric conditions on the target Lorentzian manifold or small energy of the initial maps. The result implies the existence of a harmonic map in a given homotopy class with fixed boundary data.
