9 papers · 1 filter
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 vanishing of the fundamental gap of convex domains in
Theodora Bourni, Julie Clutterbuck, Xuan Hien Nguyen +3
For the Laplace operator with Dirichlet boundary conditions on convex domains in , , we prove that the product of the fundamental gap with the square of the d…
Ancient solutions for flow by powers of the curvature in
Theodora Bourni, Julie Clutterbuck, Xuan Hien Nguyen +3
We construct a new compact convex embedded ancient solution of the flow in , that lies between two parallel lines. Using this solution we class…
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…
Explicit fundamental gap estimates for some convex domains in
Theodora Bourni, Julie Clutterbuck, Xuan Hien Nguyen +3
Motivated by an example of Shih, we compute the fundamental gap of a family of convex domains in the hyperbolic plane , showing that for some of them $λ_2 - λ_1 < \fra…
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…