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Minimal surfaces in metric spaces

The main goals of the project are as follows:

  1. Solve the asymptotic Plateau problem in nonpositively, respectively negatively curved spaces / groups. Analyze solutions and find applications.
  2.  Study conformal changes of spaces with upper curvature bounds and find a new approach to Reshetnyak's theory of surfaces with upper curvature bounds.
  3. Investigate the analytical, geometrical and topological properties of geodesic surfaces with quadratic isoperimetric inequalities and study the compactification of the class of such surfaces.
  4. Find optimal isoperimetric inequalities for curves in normed spaces and applications to regularity of minimal surfaces.
  5. Construct minimal surfaces in metric spaces by topological methods and / or min-max techniques.

Publications


    Team Members

    Dr. Stephan Stadler
    Project leader
    Ludwig-Maximilians-Universität München
    stadler(at)math.lmu.de

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