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Journal für die reine und angewandte Mathematik

Managing Editor: Weissauer, Rainer

Ed. by Colding, Tobias / Huybrechts, Daniel / Hwang, Jun-Muk / Williamson, Geordie

IMPACT FACTOR 2018: 1.859

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Mathematical Citation Quotient (MCQ) 2017: 1.49

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Volume 2017, Issue 733


Convergence to equilibrium of gradient flows defined on planar curves

Matteo Novaga / Shinya Okabe
Published Online: 2015-06-05 | DOI: https://doi.org/10.1515/crelle-2015-0001


We consider the evolution of open planar curves by the steepest descent flow of a geometric functional, with different boundary conditions. We prove that, if any set of stationary solutions with fixed energy is finite, then a solution of the flow converges to a stationary solution as time goes to infinity. We also present a few applications of this result.


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About the article

Received: 2013-11-08

Revised: 2014-12-26

Published Online: 2015-06-05

Published in Print: 2017-12-01

The second author was partially supported by the JSPS Strategic Young Researcher Overseas Visits Program for Accelerating Brain Circulation and by Grant-in-Aid for Young Scientists (B) (No. 24740097).

Citation Information: Journal für die reine und angewandte Mathematik (Crelles Journal), Volume 2017, Issue 733, Pages 87–119, ISSN (Online) 1435-5345, ISSN (Print) 0075-4102, DOI: https://doi.org/10.1515/crelle-2015-0001.

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