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Lower bounds for the first Dirichlet eigenvalue in wedge domains.

University College Cork, Ireland

The classical Faber-Krahn inequality compares the first Dirichlet eigenvalue of the Laplacian for a bounded domain to that of a ball.
I will discuss similar bounds for domains contained in wedges, both in Euclidean space and the sphere. If time allows, I will also discuss an application to Brownian pursuit. This is joint work with Andrejs Treibergs.

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