Abstract
For small-energy initial regular planar curves with generalised Neumann boundary conditions, we consider the steepest-descent gradient flow for the $L^2$-norm of the derivative of curvature with respect to arc length. We show that such curves between parallel lines converge exponentially in the $C^\infty$ topology in infinite time to straight lines.
Citation
James McCoy. Glen Wheeler. Yuhan Wu. "A sixth order flow of plane curves with boundary conditions." Tohoku Math. J. (2) 72 (3) 379 - 393, 2020. https://doi.org/10.2748/tmj/1601085621
Information