Plateau flow

Michael Struwe (ETH Zurich)

E1 05 (Leibniz-Saal)

Abstract

Using the Millot-Sire 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 $N \subset \R^{n}$ , recently studied by Wettstein, and for arbitrary finite-energy data we obtain a result fully analogous to the classical results for the harmonic map heat flow of surfaces and in similar generality. When $N$ is a smoothly embedded, oriented closed curve $Γ \subset \R^{n}$ the half-harmonic map heat flow may be viewed as an alternative gradient flow for the Plateau problem of disc-type minimal surfaces.

Links

conference

16.05.22 25.05.22

Mathematical Concepts in the Sciences and Humanities Mathematical Concepts in the Sciences and Humanities

MPI für Mathematik in den Naturwissenschaften Leipzig (Leipzig) E1 05 (Leibniz-Saal) Live Stream

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Katharina Matschke

Max Planck Institute for Mathematics in the Sciences, Germany Contact via Mail

Nihat Ay

Hamburg University of Technology, Germany and Santa Fe Institute

Eckehard Olbrich

Max Planck Institute for Mathematics in the Sciences, Germany

Felix Otto

Max Planck Institute for Mathematics in the Sciences, Germany

Bernd Sturmfels

Max Planck Institute for Mathematics in the Sciences, Germany