2 citations · 2 across the 6 of their papers we have counts for
8 papers
Spectral gaps of double covers of hyperbolic surfaces
Lawford Hatcher, Bram Petri
We prove that, in most moduli spaces of orientable hyperbolic surfaces of finite area, there exist surfaces all of whose covers of degree two have a new small eigenvalue. On the ot…
Hot spots in convex hyperbolic planar domains with small eigenvalues
Lawford Hatcher
We prove a variant of Rauch's hot spots conjecture for hyperbolic planar domains with small Neumann or mixed Dirichlet-Neumann eigenvalues. We conclude, for instance, that on bound…
Hot spots in domains of constant curvature
Lawford Hatcher
We prove constant-curvature analogues of several results regarding the hot spots conjecture in dimension two. Our main theorem shows that the hot spots conjecture holds for all non…
Hot spots on cones and warped product manifolds
Lawford Hatcher
We study extrema of solutions to the heat equation (i.e. hot spots) on a class of warped product manifolds of the form where is a closed Riem…
Geometric inequalities between Dirichlet and Neumann eigenvalues
Lawford Hatcher
Comparing Neumann and Dirichlet eigenvalues of the Laplacian on a bounded domain $Ω\subseteq\Rbb^n$ is a topic that goes back at least to the work of Pólya \cite{polya}. We study t…
A hot spots theorem for the mixed eigenvalue problem with small Dirichlet region
Lawford Hatcher
We prove that on convex domains, first mixed Laplace eigenfunctions have no interior critical points if the Dirichlet region is connected and sufficiently small. We also find two s…
The hot spots conjecture for some non-convex polygons
Lawford Hatcher
We give an elementary new proof of the hot spots conjecture for L-shaped domains. This result, in addition to a new eigenvalue inequality, allows us to locate the hot spots in Swis…
First mixed Laplace eigenfunctions with no hot spots
Lawford Hatcher
The hot spots conjecture of J. Rauch states that the second Neumann eigenfunction of the Laplace operator on a bounded Lipschitz domain in attains its extrema only o…