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Research talks;Analysis and its Applications;Partial Differential Equations;Dynamical Systems and Ordinary Differential Equations;Geometry
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.
58J50 ; 35P05 ; 11F72
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