Sinica-NCTS Geometry Seminar
主講者: | Professor María del Mar González Nogueras(Universitat Politècnica de Catalunya) |
講題: | Fractional Laplacians on hyperbolic space |
時間: | 2013-02-01 (Fri.) 16:00 - 17:00 |
地點: | 數學所 617 研討室 (台大院區) |
Abstract: | We give a definition of the fractional Laplacian on hyperbolic space (and on some other noncompact manifolds) through an extension problem introduced by Caffarelli-Silvestre, that allows to construct an explicit convolution kernel and to show a trace Sobolev inequality for the operator. The main difficulty is to have a precise control of the decay of the metric at infinity. Then we consider some semilinear equations on hyperbolic space, for which prove the existence of heteroclinic connections in the following sense: a so-called layer solution is a smooth solution converging to $\pm 1$ at any point of the two hemispheres $S_{\pm}\subset \partial_\infty \mathbb H^n$ and which is strictly increasing with respect to the signed distance to a totally geodesic hyperplane. |
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