64 citations · 130 across the 28 of their papers we have counts for
32 papers
Gaps between consecutive eigenvalues for compact metric graphs
David Borthwick, Evans M. Harrell, Haozhe Yu
On a compact metric graph, we consider the spectrum of the Laplacian defined with a mix of standard and Dirichlet vertex conditions. A Cheeger-type lower bound on the gap $λ_2 - λ_…
The heat kernel on the diagonal for a compact metric graph
David Borthwick, Kenny Jones, Evans M. Harrell
We analyze the heat kernel associated to the Laplacian on a compact metric graph, with standard Kirchoff-Neumann vertex conditions. An explicit formula for the heat kernel as a sum…
Existence of resonances for Schrodinger operators on hyperbolic space
David Borthwick, Yiran Wang
We prove existence results and lower bounds for the resonances of Schrödinger operators associated to smooth, compactly support potentials on hyperbolic space. The results are deri…
Sharp diameter bound on the spectral gap for quantum graphs
David Borthwick, Livia Corsi, Kenny Jones
We establish an upper bound on the spectral gap for compact quantum graphs which depends only on the diameter and total number of vertices. This bound is asymptotically sharp for p…
Existence and stability of Schrödinger solitons on noncompact manifolds
David Borthwick, Roland Donninger, Enno Lenzmann +1
We consider the focusing nonlinear Schrödinger equation on a large class of rotationally symmetric, noncompact manifolds. We prove the existence of a solitary wave by perturbing of…
Improved fractal Weyl bounds for hyperbolic manifolds
Semyon Dyatlov, David Borthwick, Tobias Weich
We give a new fractal Weyl upper bound for resonances of convex co-compact hyperbolic manifolds in terms of the dimension of the manifold and the dimension of its limit set…