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arXiv · 1506.07567

Entropy, stability, and harmonic map flow

Jess Boling·Casey Lynn Kelleher·Jeffrey Streets
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Abstract

Inspired by work of Colding-Minicozzi on mean curvature flow, Zhang introduced a notion of entropy stability for harmonic map flow. We build further upon this work in several directions. First we prove the equivalence of entropy stability with a more computationally tractable $\mathcal F$-stability. Then, focusing on the case of spherical targets, we prove a general instability result for high-entropy solitons. Finally, we exploit results of Lin-Wang to observe long time existence and convergence results for maps into certain convex domains and how they relate to generic singularities of harmonic map flow.

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Jess Boling, Casey Lynn Kelleher, Jeffrey Streets. 2015-06-24. Entropy, stability, and harmonic map flow. https://arxiv.org/abs/1506.07567

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