Laplacians, metrics and boundaries of simplicial complexes and Dirichlet spaces

We explore the connection between the analysis of operators with the geometry and the boundary of the space.  The operators in questions are Laplacians, the geometrical input comes via an intrinsic metric of the Laplacian and the boundary typically arises abstractly from the Laplacian via potential theory and harmonic functions. The two directions give rise to the following two parts of the project:
(A)  Higher order Laplacians on simplicial complexes.
(B)  Harmonic functions of Laplacians arising from Dirichlet spaces.


    Team Members

    Prof. Dr. Matthias Keller
    Project leader
    Universität Potsdam

    Prof. Dr. Daniel Lenz
    Project leader
    Friedrich-Schiller-Universität Jena

    Dr. Marcel Schmidt
    Researcher, Project leader
    Friedrich-Schiller-Universität Jena

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