6 papers
Minimal equators and homological systoles in Berger projective spaces
Glen Wheeler
Gil-Medrano asked whether real projective subspaces remain minimal and volume-minimising under Berger deformations in dimensions greater than three. We answer the minimality questi…
A simply connected nilpotent Lie group with a closed geodesic
Glen Wheeler
We give a six-dimensional simply connected nilpotent Lie group together with a left-invariant Riemannian metric admitting a nonconstant closed geodesic. The example gives a positiv…
On the planar free elastic flow with small oscillation of curvature
Ben Andrews, Glen Wheeler
The free elastic flow that begins at any closed curve exists for all time. If the initial curve is an -fold covered circle (``-circle'') the solution expands self-similarly…
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…
Jellyfish exist
Ben Andrews, Glen Wheeler
We show the existence of infinitely many geometrically distinct homothetic expanders (jellyfish) for the elastic flow, epicyclic shrinkers for the curve diffusion flow, and epicycl…
The curve-lengthening flow in inversive geometry
Ben Andrews, Glen Wheeler
We consider an invariant gradient flow for the invariant length functional for co-compact curves in inversive geometry, and prove that solutions exist for all time and converge to…