A well-known discretization of the Laplace operator is the graph Laplacian, whose spectrum reflects several interesting combinatorial properties of graphs. Can one find a discretization of the Laplace(-Beltrami) operator that would also reflect geometric properties of the domain/manifold? An answer is known for triangulations of domains in the Euclidean space: the so-called cotangent Laplacian. In a recent work with Wai Yeung Lam we provided a related construction for domains on the sphere or in the hyperbolic plane. There is a natural way to extend the cotangent Laplacian to polyhedral manifolds, but many questions related to its spectrum remain unsolved.
Discrete Laplacians
09.10.2025 11:30 - 12:30
Organiser:
T. Körber, A. Molchanova, F. Rupp
Location: