Exponential convergence rate of the harmonic heat flow

DOI10.1007/S00013-022-01714-4arXiv2105.03910WikidataQ115609525 ScholiaQ115609525MaRDI QIDQ6367193

Publication date: 9 May 2021

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).

Mathematics Subject Classification ID

Nonlinear parabolic equations (35K55) Harmonic maps, etc. (58E20)

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