Skip to main content
placeholder image

A sixth order flow of plane curves with boundary conditions

Journal Article


Abstract


  • For small-energy initial regular planar curves with generalised Neumann boundary conditions, we consider the steepest-descent gradient flow for the L2-norm of the derivative of curvature with respect to arc length. We show that such curves between parallel lines converge exponentially in the C∞topology in infinite time to straight lines.

Publication Date


  • 2020

Citation


  • Mccoy, J., Wheeler, G., & Wu, Y. (2020). A sixth order flow of plane curves with boundary conditions. Tohoku Mathematical Journal, 72(3), 379-393. doi:10.2748/tmj/1601085621

Scopus Eid


  • 2-s2.0-85098267443

Start Page


  • 379

End Page


  • 393

Volume


  • 72

Issue


  • 3

Abstract


  • For small-energy initial regular planar curves with generalised Neumann boundary conditions, we consider the steepest-descent gradient flow for the L2-norm of the derivative of curvature with respect to arc length. We show that such curves between parallel lines converge exponentially in the C∞topology in infinite time to straight lines.

Publication Date


  • 2020

Citation


  • Mccoy, J., Wheeler, G., & Wu, Y. (2020). A sixth order flow of plane curves with boundary conditions. Tohoku Mathematical Journal, 72(3), 379-393. doi:10.2748/tmj/1601085621

Scopus Eid


  • 2-s2.0-85098267443

Start Page


  • 379

End Page


  • 393

Volume


  • 72

Issue


  • 3