The polyharmonic heat flow of closed plane curves
Differential Geometry
2015-05-13 v1
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^infty-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.
Keywords
Cite
@article{arxiv.1505.02877,
title = {The polyharmonic heat flow of closed plane curves},
author = {Scott Parkins and Glen Wheeler},
journal= {arXiv preprint arXiv:1505.02877},
year = {2015}
}
Comments
23 pages