6 papers · 1 filter
Zoll magnetic structures and ruled surfaces
Jan Bohr, Gabriel P. Paternain
A Zoll magnetic system on an oriented closed surface is a Riemannian metric together with a function , such that every unit speed solution of the…
Conformal boundary rigidity from null geodesic travel times
Gabriel Paternain, Eric Woolgar
The gravitational field of a distant, isolated system is manifested by the conformally invariant Weyl tensor. Thus the conformal structure far from the system encodes the system's…
Local and Global Blow Downs of Transport Twistor Space
Jan Bohr, François Monard, Gabriel P. Paternain
Transport twistor spaces are degenerate complex -dimensional manifolds that complexify transport problems on Riemannian surfaces, appearing, e.g., in geometric inverse probl…
On the interplay between the light ray and the magnetic X-ray transforms
Lauri Oksanen, Gabriel P. Paternain, Miika Sarkkinen
We study the light ray transform acting on tensors on a stationary Lorentzian manifold. Our main result is injectivity up to the natural obstruction as long as the associated magne…
Biholomorphism Rigidity for Transport Twistor Spaces
Jan Bohr, François Monard, Gabriel P. Paternain
We prove that biholomorphisms between the transport twistor spaces of simple or Anosov surfaces exhibit rigidity: they must be, up to constant rescaling and the antipodal map, the…
Marked length spectrum rigidity for Anosov surfaces
Colin Guillarmou, Thibault Lefeuvre, Gabriel P. Paternain
Let be a smooth closed oriented surface of genus . We prove that two metrics on with the same marked length spectrum and Anosov geodesic flow are isometric via an…