Hyperbolic triangles with no positive Neumann eigenvalues
Apparaît également dans la collection : Evolution equations on singular spaces / Équations d'évolution sur les espaces singuliers
In joint work with Luc Hillairet, we show that the Laplacian associated with the generic finite area triangle in hyperbolic plane with one vertex of angle zero has no positive Neumann eigenvalues. This is the first evidence for the Phillips-Sarnak philosophy that does not depend on a multiplicity hypothesis. The proof is based an a method that we call asymptotic separation of variables.