Seminar

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.
Organizers
Søren Fournais
Aarhus University
Rupert Frank
LMU Munich
Benjamin Schlein
University of Zurich, UZH
Simone Warzel
TU Munich

Program
Contact

Rupert Frank

frank@math.lmu.de

Other
information

For practical matters at the Institute, send an e-mail to administration@mittag-leffler.se