2019/09/13 by James Kohout, Kohout, James, Melanie Rupflin +3
Mathematics · #Geometric Analysis and Curvature Flows #Mathematical Dynamics and Fractals #Geometry and complex manifolds
paper · pdf · doi:10.48550/arxiv.1909.06422
The harmonic map energy of a map from a closed, constant-curvature surface to a closed target manifold can be seen as a functional on the space of maps and domain metrics. We consider the gradient flow for this energy. In the absence of singularities, previous theory established that the flow converges to a branched minimal immersion, but only at a sequence of times converging to infinity, and only after pulling back by a sequence of diffeomorphisms. In this paper we investigate whether it is necessary to pull back by these diffeomorphisms, and whether the convergence is uniform as time tends to infinity.