3 citations · 3 across the 5 of their papers we have counts for
8 papers
On the Existence of Stable Unduloids of Dimension Eight
David Hartley
In this paper we study the stability of -dimensional constant mean curvature unduloids embedded in slabs in . We prove that among the family of half period und…
Dislocations of arbitrary topology in Coulomb eigenfunctions
Alberto Enciso, David Hartley, Daniel Peralta-Salas
For any finite link in we prove the existence of a high-energy complex-valued eigenfunction of the hydrogen atom such that its nodal set contains a union of conn…
Stability of Geodesic Spheres in under Constrained Curvature Flows
David Hartley
In this paper we discuss the stability of geodesic spheres in under constrained curvature flows. We prove that under some standard assumptions on the speed and w…
Laplace operators with eigenfunctions whose nodal set is a knot
Alberto Enciso, David Hartley, Daniel Peralta-Salas
We prove that, given any knot in a compact 3-manifold M, there exists a Riemannian metric on M such that there is a complex-valued eigenfunction u of the Laplacian, correspondi…
A problem of Berry and knotted zeros in the eigenfunctions of the harmonic oscillator
Alberto Enciso, David Hartley, Daniel Peralta-Salas
We prove that, given any finite link L in R^3, there is a high energy complex-valued eigenfunction of the harmonic oscillator such that its nodal set contains a union of connected…
Stability of near cylindrical stationary solutions to weighted-volume preserving curvature flows
David Hartley
In this paper we consider a class of weighted-volume preserving curvature flows acting on hypersurfaces that are trapped within two parallel hyperplanes and satisfy an orthogonal b…
Motion by Mixed Volume Preserving Curvature Functions Near Spheres
David Hartley
In this paper we investigate the flow of surfaces by a class of symmetric functions of the principal curvatures with a mixed volume constraint. We consider compact surfaces without…
Motion by Volume Preserving Mean Curvature Flow Near Cylinders
David Hartley
Center manifold analysis can be used in order to investigate the stability of the stationary solutions of various PDEs. This can be done by considering the PDE as an ODE between ce…