BIRS Workshop Lecture Videos
Spectral densification for hyperbolic surfaces Dyatlov, Semyon
Let M_t, t\neq 0 be a family of compact hyperbolic surfaces which as t\to 0 degenerates to a surface M_0 with two cusps, via pinching a neck. We show a quantization condition for eigenvalues of the Laplacian on M_t in compact subsets of (1/4, \infty), with the subprincipal term determined from the scattering matrix of M_0. We use the Lefschetz fibration model for the degeneration and its metric resolution due to Melrose-Zhu. This is work in progress joint with Richard Melrose.
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