Pressure metric in the space of Riemannian metrics

https://hu-berlin.zoom.us/j/61686623112
Contact: Gaetan Borot
 

We investigate the pressure metric defined in the space of
negatively curved Riemannian metrics proposed by Guillarmou, Knieper and
Lefeuvre in the Blaschke locus that contains the Teichmuller space. This
locus contains all Blaschke metrics arisen from affine geometry and is
naturally related to the Hitchin component in PGL(3,R). We study a
family of geodesics in this locus with respect to the pressure metric
and show that they have infinite lengths. This is joint work in progress
with Nikolaos Eptaminitakis.