18 apr 2023 -- 11:30   [open in google calendar]

Centro de Giorgi, Sala Conferenze

Abstract.

We will discuss some recent progress on the conformally prescribed scalar curvature problem in case of a negative Yamabe invariant, which is resolved, if the function K to be prescribed is strictly negative, while necessary and sufficient conditions are known, if K is nowhere positive. On the other hand, if K is sign changing, little is known in general beyond smallness assumptions on the max(K,0). We address the latter case variationally, still in the realm of smallness assumptions, and shed some light on the underlying features of the problem. The presented techniques do not only allow to recover, what is known up to now, in a quite natural way, but also adds some new existence results. Time permitting, we shall expose, what happens, if the smallness assumptions fail.

In collaboration with Chaona Zhu, University Tor Vergata, Rome, Italy.