Speaker:  Padi Fuster, U of Colorado, Boulder

Title: The restriction of the Laplace operator on manifolds

Abstract: On a Riemannian manifold, there is no canonical Laplace operator for vector fields or forms, and it is not clear what is the “correct” Laplacian to use when formulating fluid dynamics equations. In this talk, we will walk through different approaches for obtaining a viscosity operator when considering a Riemannian submanifold in , as well as present some concrete examples with the recent extension of the Gauss formula for the Laplace operator on hypersurfaces by Chan and Czubak (2023). Finally, we will present preliminary results on the derivation of an intrinsic viscosity operator on an ellipsoid by using a heuristic of the thin shell limit.