Exponential convergence rate of the harmonic heat flow

Ivo Slegers

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arXiv · 2105.03910

Exponential convergence rate of the harmonic heat flow

Ivo Slegers

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Abstract

We consider the harmonic heat flow for maps from a compact Riemannian manifold into a Riemannian manifold that is complete and of non-positive curvature. We prove that if the harmonic heat flow converges to a limiting harmonic map that is a non-degenerate critical point of the energy functional, then the rate of convergence is exponential (in the $L^2$ norm).

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Ivo Slegers. 2021-05-09. Exponential convergence rate of the harmonic heat flow. https://arxiv.org/abs/2105.03910

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