Sinica-NCTS Geometry Seminar

主講者: Professor Roger Moser (University of Bath, UK)
講題: Fractional harmonic maps
時間: 2010-12-06 (Mon.)  15:00 - 16:00
地點: 數學所 617 研討室 (台大院區)
Abstract:  A harmonic map between two Riemannian manifolds is a critical point of the Dirichlet energy, i.e., of a functional involving the first derivative. It is sometimes desirable to use a derivative of a different order, or perhaps a pseudo-differential operator of fractional order. It is not immediately clear, however, how to obtain a functional that is geometrically meaningful. Furthermore, the resulting problems tend to be challenging. For order 1/2, a possible approach is to interpret the maps as traces of harmonic maps. Then we can use all the results from the harmonic map theory to analyse the solutions of the problem. In principle, this also works for order m/2.
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