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Diffusion determines the compact manifold

W. Arendt, A. F. M. ter Elst Banach Center Publications 112 (2017) MSC: 58J53, 35P05, 47F05, 35R30. DOI: 10.4064/bc112-0-1


We provide a short proof for the theorem that two compact Riemannian manifolds are isometric if and only there exists an order isomorphism which intertwines between the heat semigroups on the manifolds.


  • W. ArendtAbteilung Angewandte Analysis
    Universität Ulm
    Helmholtzstr. 18
    89069 Ulm, Germany
  • A. F. M. ter ElstDepartment of Mathematics
    University of Auckland
    Private bag 92019
    Auckland 1142, New Zealand

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