Mathematikgebäude, Raum 511

Unique continuation principles constitute a very active field in control theory or the theory of random Schroedinger operators. Usually, such ucp are proved by Carleman estimates applied to generalized eigenfunctions. Carleman estimates usually depend on ellipticity and Lipschitz assumptions on the symbol of the partial differential operator under consideration. In the case of Riemannian manifolds there exist Carleman estimates and ucp for the Laplace-Beltrami operator similar to elliptic operators in $\mathbb{R}^d$. Those depend of course on elliptic and Lipschitz assumptions on the given Riemannian tensor. This circumstance makes it impossible to derive ucp depending on curvature restrictions, since it is not known how, e.g., Ricci curvature restrictions translate into uniform assumptions for the metric. I will present ucp for non-negatively Ricci curved manifolds as well as compact manifolds with Ricci curvature bounded below for small energies without using Carleman. This is joint work in progress with Martin Tautenhahn.

Dr. Christian Rose

MPI Leipzig