Gabriel Paternain

Carleman estimates for geodesic X-ray transforms.

I will describe a new energy estimate for the geodesic vector field
of a manifold of negative curvature. The estimate has several
applications including
injectivity of non-abelian X-ray transforms and the existence of
invariant distributions with prescribed first Fourier coefficients
for the geodesic flow. This is joint work with Mikko Salo.