Endpoint resolvent estimates for compact Riemannian manifolds
Spectral Methods in Mathematical Physics
30 January 17:00 - 18:00
Lukas Schimmer - University of Copenhagen
In this talk I will give an introduction to resolvent estimates. In particular, I will discuss L_p -> L_p' bounds for the resolvent of the Laplace–Beltrami operator on a compact Riemannian manifold of dimension n and will present a proof in the endpoint case p = 2(n + 1)/(n + 3). The bounds have the same behaviour with respect to the spectral parameter as their Euclidean analogue, due to Kenig, Ruiz and Sogge, provided a parabolic neighbourhood of the positive half-line is removed. If time permits, I will show that this region is optimal, for instance, in the case of a sphere. This is based on joint work with R. Frank.
University of Zurich, UZH