26 citations · 61 across the 17 of their papers we have counts for
18 papers
Convexity inequalities for eigenvalues and log-concavity of eigenfunctions
Paul Bryan, Julie Clutterbuck, Cale Rankin
We give simple new proofs of two well-known results for the Schrödinger operator: first, the Brunn--Minkowski inequality for Dirichlet eigenvalues and, second, the log-concavity of…
Constant potentials do not minimise the fundamental gap on convex domains in hyperbolic space
Julie Clutterbuck, Frieder Jäckel, Xuan Hien Nguyen
We show that for every and there exist a convex domain with diameter and a convex potential on such that the fundamental gap…
Local Spectral Optimisation for Robin Problems with Negative Boundary Parameter on Quadrilaterals
Julie Clutterbuck, James Larsen-Scott
We investigate the Robin eigenvalue problem for the Laplacian with negative boundary parameter on quadrilateral domains of fixed area. In this paper, we prove that the square is a…
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…
The fundamental gap for a one-dimensional Schrödinger operator with Robin boundary conditions
Ben Andrews, Julie Clutterbuck, Daniel Hauer
For Schrödinger operators on an interval with either convex or symmetric single-well potentials, and Robin or Neumann boundary conditions, the gap between the two lowest eigenvalue…