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Caltech/UCLA Joint Analysis Seminar

Friday, April 22, 2016
5:00pm to 6:00pm
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Off Campus
Harmonic maps and heat flows on hyperbolic spaces
Marius Lemm, Graduate Student, Mathematics, Caltech,
We prove that any quasi-conformal map of the (n−1)-dimensional sphere when n > 2 can be extended to a smooth quasi-isometry F of the n-dimensional hyperbolic space such that the heat flow starting with F converges to a quasi-isometric harmonic map. This implies the Schoen-Li-Wang conjecture that every quasi-conformal map of the (n−1)-sphere can be extended to a harmonic quasi-isometry when n > 2 (that result was recently proved for n=2,3 without proving convergence of the heat flow). The main tools to show the convergence of the heat flow are the Hamilton parabolic maximum principle for sub-solutions of the heat equation, the diffusion of heat in hyperbolic space and the Mostow rigidity. This is joint work with Vladimir Markovic.

The location is MS6221 UCLA.

For more information, please contact Mathematics Department by phone at 626-395-4335 or by email at [email protected].