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math.DG2026
Heintze-Karcher and Reverse Alexandrov-Fenchel Inequalities via Focal Geometry
Kwok-kun Kwong, Scott Parkins, Glen Wheeler
We prove a collection of reverse Alexandrov-Fenchel type inequalities in anisotropic, Euclidean, spherical, and hyperbolic settings. The unifying principle is that the relevant def…
math.DG2017★ 1 cited
The anisotropic polyharmonic curve flow for closed plane curves
Scott Parkins, Glen Wheeler
We study the curve diffusion flow for closed curves immersed in the Minkowski plane , which is equivalent to the Euclidean plane endowed with a closed, symmetric, conv…
math.DG2015
The polyharmonic heat flow of closed plane curves
Scott Parkins, Glen Wheeler
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 curv…