Descrizione
Martin Mayer, Scuola Superiore Meridionale, Naples, Italy

“The prescribed scalar curvature problem in the negative Yamabe case ”

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 adress 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 exemplify, what happens,
if the smallness assumptions fail.
In collaboration with Chaona Zhu, University Tor Vergata, Rome, Italy.