33 citations · 181 across the 33 of their papers we have counts for
42 papers
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…
Rigidity and stability for the Bogovskii constant
Glen Wheeler
We prove that balls are the unique minimisers of the Bogovskii constant among bounded connected Lipschitz domains in , , resolving Open Problem 2 of Gazzola,…
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\…
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…
Convergence of solutions to a convective Cahn-Hilliard type equation of the sixth order in case of small deposition rates
Piotr Rybka, Glen Wheeler
We show stabilisation of solutions to the sixth-order convective Cahn-Hilliard equation. {The problem} has the structure of a gradient flow perturbed by a quadratic destabilising t…
The -elastic flow for planar closed curves with constant parametrization
Shinya Okabe, Glen Wheeler
In this paper, we consider the -gradient flow for the modified -elastic energy defined on planar closed curves. We formulate a notion of weak solution for the flow and prov…
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…
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…
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…
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…
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…
A sixth order flow of plane curves with boundary conditions
James McCoy, Glen Wheeler, Yuhan Wu
We show that small energy curves under a particular sixth order curvature flow with generalised Neumann boundary conditions between parallel lines converge exponentially in the smo…
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…
Curve diffusion and straightening flows on parallel lines
Glen Wheeler, Valentina-Mira Wheeler
In this paper, we study families of immersed curves with free boundary supported on parallel lines $\{η_1, η_2\}:\mathbb{R}\rightarrow\…
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…