分野別セミナー

Fractional harmonic maps are defined as harmonic maps with respect to the fractional Laplacian. In this talk, we will elaborate the methodology to tackle some problems concerning fractional harmonic maps by techniques from stochastic analysis. We will provide a characterization of harmonic maps for non-local Dirichlet forms through stochastic processes. As simple applications of this approach, we will consider the Liouville-type theorem for fractional harmonic maps with values on a unit circle and the relation between the singularities of martingales on manifolds and those of harmonic maps.