Entropy, stability and harmonic map flow
Authors:
Jess Boling, Casey Kelleher and Jeffrey Streets
Journal:
Trans. Amer. Math. Soc. 369 (2017), 5769-5808
MSC (2010):
Primary 53C43, 53C44
DOI:
https://doi.org/10.1090/tran/6949
Published electronically:
April 24, 2017
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Abstract | References | Similar Articles | Additional Information
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 -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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Additional Information
Jess Boling
Affiliation:
Department of Mathematics, Rowland Hall, University of California, Irvine, California 92617
Email:
jboling@uci.edu
Casey Kelleher
Affiliation:
Department of Mathematics, Rowland Hall, University of California, Irvine, California 92617
Email:
clkelleh@uci.edu
Jeffrey Streets
Affiliation:
Department of Mathematics, Rowland Hall, University of California, Irvine, California 92617
Email:
jstreets@uci.edu
DOI:
https://doi.org/10.1090/tran/6949
Received by editor(s):
July 3, 2015
Received by editor(s) in revised form:
February 10, 2016
Published electronically:
April 24, 2017
Additional Notes:
The second author was supported by an NSF Graduate Research Fellowship DGE-1321846
The third author was supported by the NSF via DMS-1301864 and a Sloan Foundation Fellowship
Article copyright:
© Copyright 2017
American Mathematical Society