Entropy, stability and harmonic map flow

Boling, Jess; Kelleher, Casey; Streets, Jeffrey

doi:10.1090/tran/6949

Entropy, stability and harmonic map flow
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by Jess Boling, Casey Kelleher and Jeffrey Streets PDF

Trans. Amer. Math. Soc. 369 (2017), 5769-5808 Request permission

Abstract:

Inspired by work of Colding-Minicozzi (2012) on mean curvature flow, Zhang (2012) 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 (2008) 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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