52 citations · 270 across the 36 of their papers we have counts for
20 papers · 1 filter
The Steklov spectrum of convex polygonal domains I: spectral finiteness
Emily B. Dryden, Carolyn Gordon, Javier Moreno +2
We explore the Steklov eigenvalue problem on convex polygons, focusing mainly on the inverse Steklov problem. Our primary finding reveals that, for almost all convex polygonal doma…
Casimir energy of hyperbolic orbifolds with conical singularities
Ksenia Fedosova, Julie Rowlett, Genkai Zhang
In this article, we obtain the explicit expression of the Casimir energy for 2-dimensional Clifford-Klein space forms in terms of the geometrical data of the underlying spacetime w…
The Laplace spectrum on conformally compact manifolds
Nelia Charalambous, Julie Rowlett
We consider the spectrum of the Laplace operator acting on over a conformally compact manifold for . We prove that for this spectru…
The isospectral problem for flat tori from three perspectives
Erik Nilsson, Julie Rowlett, Felix Rydell
Flat tori are among the only types of Riemannian manifolds for which the Laplace eigenvalues can be explicitly computed. In 1964, Milnor used a construction of Witt to find an exam…
La géométrie de Bakry-Émery et l'écart fondamental
Julie Rowlett
This article is a brief presentation of results surrounding the fundamental gap. We begin by recalling Bakry-Emery geometry and demonstrate connections between eigenvalues of the L…
Eigenvalue Estimates on Bakry-Emery Manifolds
Nelia Charalambous, Zhiqin Lu, Julie Rowlett
We demonstrate lower bounds for the eigenvalues of compact Bakry-Emery manifolds with and without boundary. The lower bounds for the first eigenvalue rely on a generalised maximum…
One can hear the corners of a drum
Zhiqin Lu, Julie Rowlett
We prove that the presence or absence of corners is spectrally determined in the following sense: any simply connected domain with piecewise smooth Lipschitz boundary cannot be iso…
The sound of symmetry
Zhiqin Lu, Julie Rowlett
This note begins with an introduction to the inverse isospectral problem popularized by M. Kac's 1966 article in the American Mathematical Monthly, "Can one hear the shape of a dru…
How to hear the corners of a drum
Medet Nursultanov, Julie Rowlett, David Sher
We announce a new result which shows that under either Dirichlet, Neumann, or Robin boundary conditions, the corners in a planar domain are a spectral invariant of the Laplacian. F…
Crystallographic groups, strictly tessellating polytopes, and analytic eigenfunctions
Julie Rowlett, Max Blom, Henrik Nordell +2
The mathematics of crystalline structures connects analysis, geometry, algebra, and number theory. The planar crystallographic groups were classified in the late 19th century. One…
Polyakov formulas for conical singularities in two dimensions
Clara L. Aldana, Klaus Kirsten, Julie Rowlett
We investigate the zeta-regularized determinant and its variation in the presence of conical singularities, boundaries, and corners. For surfaces with isolated conical singularitie…
Second variation of Selberg zeta functions and curvature asymptotics
Ksenia Fedosova, Julie Rowlett, Genkai Zhang
We give an explicit formula for the second variation of the logarithm of the Selberg zeta function, , on Teichmüller space. We then use this formula to determine the asymptot…
The Neumann isospectral problem for trapezoids
Hamid Hezari, Zhiqin Lu, Julie Rowlett
We show that trapezoids with identical Neumann spectra are congruent up to rigid motions of the plane. The proof is based on heat trace invariants and some new wave trace invariant…
A Polyakov formula for sectors
Clara L. Aldana, Julie Rowlett
We consider finite area convex Euclidean circular sectors. We prove a variational Polyakov formula which shows how the zeta-regularized determinant of the Laplacian varies with res…
On the discrete spectrum of quantum layers
Zhiqin Lu, Julie Rowlett
Consider a quantum particle trapped between a curved layer of constant width built over a complete, non-compact, smooth surface embedded in . We assume…
The fundamental gap of simplices
Zhiqin Lu, Julie Rowlett
The fundamental gap conjecture was recently proven by Andrews and Clutterbuck: for any convex domain in normalized to have unit diameter, the difference between the first tw…
Eigenvalues of collapsing domains and drift Laplacians
Zhiqin Lu, Julie Rowlett
By introducing a weight function to the Laplace operator, Bakry and Émery defined the "drift Laplacian" to study diffusion processes. Our first main result is that, given a Bakry-É…
Low eigenvalues and one-dimensional collapse
Zhiqin Lu, Julie Rowlett
Our main result is that if a generic convex domain in collapses to a domain in , then the difference between the first two Dirichlet eigenvalues of the Euclidean L…
Dynamics of Asymptotically Hyperbolic Manifolds
Julie Rowlett
We prove a dynamical wave trace formula for asymptotically hyperbolic (n+1) dimensional manifolds with negative (but not necessarily constant) sectional curvatures which equates th…
Spectral Geometry and Asymptotically Conic Convergence
J. M. Rowlett
In this paper we define a new convergence called "asymptotically conic convergence" in which a smooth family of Riemannian metrics on a fixed compact manifold degenerate to a metri…