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The polyharmonic heat flow of closed plane curves

Journal Article


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Abstract


  • In this paper we consider the polyharmonic heat flow of a closed curve in the plane. Our main result is that closed initial data with initially small normalised oscillation of curvature and isoperimetric defect flows exponentially fast in the C∞C∞-topology to a simple circle. Our results yield a characterisation of the total amount of time during which the flow is not strictly convex, quantifying in a sense the failure of the maximum principle.

Publication Date


  • 2016

Citation


  • Parkins, S. & Wheeler, G. (2016). The polyharmonic heat flow of closed plane curves. Journal of Mathematical Analysis and Applications, 439 (2), 608-633.

Scopus Eid


  • 2-s2.0-84961210118

Ro Full-text Url


  • http://ro.uow.edu.au/cgi/viewcontent.cgi?article=6565&context=eispapers

Ro Metadata Url


  • http://ro.uow.edu.au/eispapers/5537

Number Of Pages


  • 25

Start Page


  • 608

End Page


  • 633

Volume


  • 439

Issue


  • 2

Place Of Publication


  • United States

Abstract


  • In this paper we consider the polyharmonic heat flow of a closed curve in the plane. Our main result is that closed initial data with initially small normalised oscillation of curvature and isoperimetric defect flows exponentially fast in the C∞C∞-topology to a simple circle. Our results yield a characterisation of the total amount of time during which the flow is not strictly convex, quantifying in a sense the failure of the maximum principle.

Publication Date


  • 2016

Citation


  • Parkins, S. & Wheeler, G. (2016). The polyharmonic heat flow of closed plane curves. Journal of Mathematical Analysis and Applications, 439 (2), 608-633.

Scopus Eid


  • 2-s2.0-84961210118

Ro Full-text Url


  • http://ro.uow.edu.au/cgi/viewcontent.cgi?article=6565&context=eispapers

Ro Metadata Url


  • http://ro.uow.edu.au/eispapers/5537

Number Of Pages


  • 25

Start Page


  • 608

End Page


  • 633

Volume


  • 439

Issue


  • 2

Place Of Publication


  • United States