2 citations · 2 across the 6 of their papers we have counts for
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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…
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…