21 citations · 67 across the 20 of their papers we have counts for
21 papers
Upper bounds for the Steklov eigenvalues of warped products
Jade Brisson, Bruno Colbois, Alexandre Girouard +1
We obtain upper bounds for the Steklov eigenvalues of warped products , where is a compact Riemannian manifold with boundary and is a closed Riemannian manifold…
Nodal counts for the Robin problem on Lipschitz domains
Katie Gittins, Asma Hassannezhad, Corentin Léna +1
We consider the Courant-sharp eigenvalues of the Robin Laplacian for bounded, connected, open sets in , , with Lipschitz boundary. We prove Pleijel's theore…
Qualitative properties of the heat content
Michiel van den Berg, Katie Gittins
We obtain monotonicity and convexity results for the heat content of domains in Riemannian manifolds and in Euclidean space subject to various initial temperature conditions. We in…
Spectral ratios and gaps for Steklov eigenvalues of balls with revolution-type metrics
Jade Brisson, Bruno Colbois, Katie Gittins
We investigate upper bounds for the spectral ratios and gaps for the Steklov eigenvalues of balls with revolution-type metrics. We do not impose conditions on the Ricci curvature o…
Do the Hodge spectra distinguish orbifolds from manifolds? Part 2
Katie Gittins, Carolyn Gordon, Ingrid Membrillo Solis +3
In \cite{GGKM-SSS} we examined the relationship between the singular set of a compact Riemannian orbifold and the spectrum of the Hodge Laplacian on -forms by computing the heat…
Eigenvalue estimates for the magnetic Hodge Laplacian on differential forms
Michela Egidi, Katie Gittins, Georges Habib +1
In this paper we introduce the magnetic Hodge Laplacian, which is a generalization of the magnetic Laplacian on functions to differential forms. We consider various spectral result…
Heat flow in polygons with reflecting edges
Sam Farrington, Katie Gittins
We investigate the heat flow in an open, bounded set in with polygonal boundary . We suppose that contains an open, bounded set w…
Upper bounds for Steklov eigenvalues of submanifolds in Euclidean space via the intersection index
Bruno Colbois, Katie Gittins
We obtain upper bounds for the Steklov eigenvalues of a smooth, compact, connected, -dimensional submanifold of Euclidean space with boundary that involve the i…
Courant-sharp Robin eigenvalues for the square: the case of negative Robin parameter
Katie Gittins, Bernard Helffer
We consider the cases where there is equality in Courant's nodal domain theorem for the Laplacian with a Robin boundary condition on the square. In our previous two papers, we trea…
Courant-sharp Robin eigenvalues for the square -- the case with small Robin parameter--
Katie Gittins, Bernard Helffer
This article is the continuation of our first work on the determination of the cases where there is equality in Courant's Nodal Domain theorem in the case of a Robin boundary condi…
Heat flow from polygons
Michiel van den Berg, Peter Gilkey, Katie Gittins
We study the heat flow from an open, bounded set in with a polygonal boundary . The initial condition is the indicator function of . A Dirichlet bound…
Courant-sharp Robin eigenvalues for the square and other planar domains
Katie Gittins, Bernard Helffer
This paper is devoted to the determination of the cases where there is equality in Courant's nodal domain theorem in the case of a Robin boundary condition. For the square, we part…
Upper bounds for Courant-sharp Neumann and Robin eigenvalues
Katie Gittins, Corentin Léna
We consider the eigenvalues of the Laplacian on an open, bounded, connected set in with boundary, with a Neumann boundary condition or a Robin boundary conditi…
Steklov eigenvalues of submanifolds with prescribed boundary in Euclidean space
Bruno Colbois, Alexandre Girouard, Katie Gittins
We obtain upper and lower bounds for Steklov eigenvalues of submanifolds with prescribed boundary in Euclidean space. A very general upper bound is proved, which depends only on th…
Asymptotic behaviour of cuboids optimising Laplacian eigenvalues
Katie Gittins, Simon Larson
We prove that in dimension , within the collection of unit measure cuboids in (i.e. domains of the form ), any sequence of minimis…
Minimising Dirichlet eigenvalues on cuboids of unit measure
Michiel van den Berg, Katie Gittins
We consider the minimisation of Dirichlet eigenvalues , , of the Laplacian on cuboids of unit measure in . We prove that any sequence of optimal cuboids in $\R…
On the number of Courant-sharp Dirichlet eigenvalues
Michiel van den Berg, Katie Gittins
We consider arbitrary open sets in Euclidean space with finite Lebesgue measure, and obtain upper bounds for (i) the largest Courant-sharp Dirichlet eigenvalue of , (ii) the…
Maximising Neumann eigenvalues on rectangles
Michiel van den Berg, Dorin Bucur, Katie Gittins
We obtain results for the spectral optimisation of Neumann eigenvalues on rectangles in with a measure or perimeter constraint. We show that the rectangle with measu…
On the heat content of a polygon
Michiel van den Berg, Katie Gittins
Let be a bounded, connected, open set in Euclidean space with polygonal boundary. Suppose has initial temperature and the complement of has initial…
Uniform bounds for the heat content of open sets in Euclidean space
Michiel van den Berg, Katie Gittins
We obtain (i) lower and upper bounds for the heat content of an open set in with -smooth boundary and finite Lebesgue measure, (ii) a necessary and sufficient geo…
Some spectral applications of McMullen's Hausdorff dimension algorithm
K. Gittins, N. Peyerimhoff, M. Stoiciu +1
Using McMullen's Hausdorff dimension algorithm, we study numerically the dimension of the limit set of groups generated by reflections along three geodesics on the hyperbolic plane…