Tohoku Mathematical Journal
2020
September
SECOND SERIES VOL. 72, NO. 3

Tohoku Math. J.
72 (2020), 379-393

Title A SIXTH ORDER FLOW OF PLANE CURVES WITH BOUNDARY CONDITIONS

Author James Mccoy, Glen Wheeler and Yuhan Wu

(Received March 22, 2018, revised January 22, 2019)
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.

Mathematics Subject Classification. Primary 53C44.
Key words and phrases. Curvature flow, sixth order parabolic equation, Neumann boundary condition.

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