PLATEAU FLOW OR THE HEAT FLOW FOR HALF-HARMONIC MAPS

Using the interpretation of the half-Laplacian on S 1 as the Dirichlet-to-Neumann operator for the Laplace equation on the ball B , we devise a classical approach to the heat flow for half-harmonic maps from S 1 to a closed target manifold N subset of R n , recently studied by Wettstein, and for arbitrary finite-energy data we obtain a result fully analogous to the author's 1985 results for the harmonic map heat flow of surfaces and in similar generality. When N is a smoothly embedded, oriented closed curve F subset of R n , the half-harmonic map heat flow may be viewed as an alternative gradient flow for a variant of the Plateau problem of disc-type minimal surfaces.