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Open ended seminar: Measures on the boundary minimizing energy April 21, 2015 (02:00 PM PDT - 04:30 PM PDT)
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Location: MSRI: Baker Board Room
Speaker(s) Seonhee Lim (Seoul National University)
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Let X be the universal cover of a compact manifold of negative curvature. We will present local limit theorem of the heat kernel and explain how we use equidistribution of large spheres. The equidistribution is based on uniform mixing of geodesic flow with respect to a conformal family of measures on the boundary of X, which is the family associated to the Martin kernel. 


This family of measures turns out to be the unique family of measures minimizing the energy (or the Rayleigh quotient of Mohsen). We will also look at the generalized Harish-Chandra function. The normalizing constant which can be defined for any conformal family depends only on the cohomology class of the family of measures.


This is a joint work with François Ledrappier.

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