6 papers
A multi-point maximum principle to prove the global Harnack inequality for the doubly nonlinear heat equation
Ben Andrews, Daniel Hauer, Jessica Slegers
This work aims to present a new proof of the global pointwise Harnack inequality satisfied by positive viscosity solutions of the doubly nonlinear heat equation on .…
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…
A multi-point maximum principle to prove global Harnack inequalities for Schrödinger operators
Ben Andrews, Daniel Hauer, Jessica Slegers
In this article, we introduce a new methodology to prove global parabolic Harnack inequalities on Riemannian manifolds. We focus on presenting a new proof of the global pointwise H…
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.…
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…
Strategies in a misère two-player tree searching game
Ben Andrews
In this paper, we analyse a misere tree searching game, where players take turns to guess vertices in a tree with a secret `poisoned' vertex. After each turn, the guessed vertex is…