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Abstract
We consider regular open curves in ℝn with fixed boundary points, curvature equal to zero at the boundary, subject to a fixed length constraint and moving according to the L2-gradient flow of the elastic energy. For this flow we prove a long-time existence result and subconvergence to critical points.
Keywords: Geometric evolution equation; fourth order problem; natural boundary conditions; elastic energy; Willmore functional
Received: 2013-11-11
Accepted: 2014-2-10
Published Online: 2014-5-28
Published in Print: 2014-6-28
©2014 Walter de Gruyter Berlin/Boston