33 citations · 181 across the 33 of their papers we have counts for
29 papers · 1 filter
The Cartan-Hadamard isoperimetric inequality under controlled variation of curvature
Glen Wheeler
We prove the Cartan-Hadamard conjecture (the sharp Euclidean isoperimetric inequality) in every dimension, assuming that the sectional curvature is pinched relative to a reference…
Pinchoff by surface diffusion
Glen Wheeler
We construct surface diffusion flows that drive smooth closed embedded tori to pinchoff in finite time. The flow remains embedded for $t\…
On an inverse curvature flow in two-dimensional space forms
Kwok-Kun Kwong, Yong Wei, Glen Wheeler +1
We study the evolution of compact convex curves in two-dimensional space forms. The normal speed is given by the difference of the weighted inverse curvature with the support funct…
On the -gradient flow for the length functional
Philip Schrader, Glen Wheeler, Valentina-Mira Wheeler
In this article we consider the length functional defined on the space of immersed planar curves. The Riemannian metric gives rise to the curve shortening flow as the gra…
The gradient flow for entropy on closed planar curves
Lachlann O'Donnell, Glen Wheeler, Valentina-Mira Wheeler
In this paper we consider the steepest descent L2-gradient flow of the entropy functional. The flow expands convex curves, with the radius of an initial circle growing like the squ…
Convergence for global curve diffusion flows
Glen Wheeler
In this note we establish exponentially fast smooth convergence for global curve diffusion flows, and discuss open problems relating embeddedness to global existence (Giga's conjec…
Theory and numerics for Chen's flow of curves
Matthew Cooper, Glen Wheeler, Valentina-Mira Wheeler
In this article we study Chen's flow of curves from theoreical and numerical perspectives. We investigate two settings: that of closed immersed -circles, and immersed lines sati…
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…
A rigidity theorem for ideal surfaces with flat boundary
James McCoy, Glen Wheeler
We consider surfaces with boundary satisfying a sixth order nonlinear elliptic partial differential equation corresponding to extremising the -norm of the gradient of the mean…
Analysis of the Inhomogeneous Willmore Equation
Yann Bernard, Glen Wheeler, Valentina-Mira Wheeler
We study a class of fourth-order geometric problems modelling Willmore surfaces, conformally constrained Willmore surfaces, isoperimetrically constrained Willmore surfaces, bi-harm…
A gradient flow for the p-elastic energy defined on closed planar curves
Shinya Okabe, Paola Pozzi, Glen Wheeler
We study the evolution of closed inextensible planar curves under a second order flow that decreases the -elastic energy. A short time existence result for is…
Closed ideal planar curves
Ben Andrews, James McCoy, Glen Wheeler +1
In this paper we use a gradient flow to deform closed planar curves to curves with least variation of geodesic curvature in the sense. Given a smooth initial curve we show th…
On a curvature flow model for embryonic epidermal wound healing
Shuhui He, Glen Wheeler, Valentina-Mira Wheeler
The paper studies a curvature flow linked to the physical phenomenon of wound closure. Under the flow we show that a closed, initially convex or close-to-convex curve shrinks to a…
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…
Concentration-compactness and finite-time singularities for Chen's flow
Yann Bernard, Glen Wheeler, Valentina-Mira Wheeler
Chen's flow is a fourth-order curvature flow motivated by the spectral decomposition of immersions, a program classically pushed by B.-Y. Chen since the 1970s. In curvature flow te…
Minimal hypersurfaces in the ball with free boundary
Glen Wheeler, Valentina-Mira Wheeler
In this note we use the strong maximum principle and integral estimates prove two results on minimal hypersurfaces with free boundary on the stan…
Mean curvature flow with free boundary - Type 2 singularities
Glen Wheeler, Valentina-Mira Wheeler
In this paper we give sufficient conditions that guarantee the meancurvature flow with free boundary on an embedded rotationally symmetric double cone develops a Type 2 curvature s…
The shrinking figure eight and other solitons for the curve diffusion flow
Maureen Edwards, Alexander Gerhardt-Bourke, James McCoy +2
In this article we investigate the dynamics of special solutions to the surface diffusion flow of idealised ribbons. This equation reduces to studying the curve diffusion flow for…
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…
Solitons for the inverse mean curvature flow
Gregory Drugan, Hojoo Lee, Glen Wheeler
We investigate self-similar solutions to the inverse mean curvature flow in Euclidean space. In the case of one dimensional planar solitons, we explicitly classify all homothetic s…
Mean curvature flow with free boundary outside a hypersphere
Glen Wheeler, Valentina-Mira Wheeler
The purpose of this paper is twofold: firstly, to establish sufficient conditions under which the mean curvature flow supported on a hypersphere with exterior Dirichlet boundary ex…
Willmore flow of surfaces in Riemannian spaces I: Concentration-compactness
Jan Metzger, Glen Wheeler, Valentina-Mira Wheeler
In this paper we study the local regularity of closed surfaces immersed in a Riemannian 3-manifold flowing by Willmore flow. We establish a pair of concentration-compactness altern…
Chen's conjecture and epsilon-superbiharmonic submanifolds of Riemannian manifolds
Glen Wheeler
B.-Y. Chen famously conjectured that every submanifold of Euclidean space with harmonic mean curvature vector is minimal. In this note we establish a much more general statement fo…
Global analysis of the generalised Helfrich flow of closed curves immersed in
Glen Wheeler
In this paper we consider the evolution of regular closed elastic curves immersed in . Equipping the ambient Euclidean space with a vector field $\ca:\R^n\rightarrow\R^n$…