Prescribing constant curvatures in conformal geometry.

Andrea Malchiodi, Trieste


One of the main problems in differential geometry is to deform the metric of a given
manifold in order to obtain a "standard" structure. In conformal geometry the best one
can hope for is to control interesting scalar quantities which might give information of
the geometry/topology of the manifold.
Some bacis results on the classical uniformization and Yamabe problem (concering the
Gauss and the scalar curvatures respectively) will be reviewed, and then some more recent
progress on higher order conformally invariant equations will be presented.