22 citations · 65 across the 13 of their papers we have counts for
17 papers
Concentration-compactness for the geometric polyharmonic heat flow
James McCoy, Scott Parkins, Glen Wheeler +1
We develop a concentration-compactness theory for geometric evolution equations of arbitrarily high order, using the geometric polyharmonic heat flow of closed immersed surfaces in…
The length-constrained ideal curve flow
James McCoy, Glen Wheeler, Yuhan Wu
A recent article by the first two authors together with B Andrews and V-M Wheeler considered the so-called `ideal curve flow', a sixth order curvature flow that seeks to deform clo…
Contracting self-similar solutions of nonhomogeneous curvature flows
James McCoy
A recent article by Li and Lv considered fully nonlinear contraction of convex hypersurfaces by certain nonhomogeneous functions of curvature, showing convergence to points in fini…
Contraction of convex hypersurfaces by nonhomogeneous functions of curvature
James McCoy
A recent article Li and Lv considered contraction of convex hypersurfaces by certain nonhomogeneous functions of curvature, showing convergence to points in finite time in certain…
Higher order curvature flows of plane curves with generalised Neumann boundary conditions
James McCoy, Glen Wheeler, Yuhan Wu
We consider the parabolic polyharmonic diffusion and -gradient flows of the -th arclength derivative of curvature for regular closed curves evolving with generalised Neuman…
Length-constrained curve diffusion
James McCoy, Glen Wheeler, Yuhan Wu
We show that any initial closed curve suitably close to a circle flows under length-constrained curve diffusion to a round circle in infinite time with exponential convergence. We…