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Spectrum of Laplacian and boundaries of hyperbolic manifolds


Speaker: Seon Hee Lim, Seoul National University
Location: 2112 MSB
Start time: Tue, Nov 18 2014, 3:10PM

There are various boundaries one can define on the universal cover of a Riemannian manifold of negative curvature. We will present two of them, namely the geometric boundary and the Martin boundary, and show that they coincide for certain cases. We will also show some properties of the spectrum of the Laplacian using measures on the geometric boundary and a generalized idea of Margulis related to counting geodesic paths.