Lorenzo Mazzieri(SISSA Trieste)

"On the singular σk-Yamabe problem"

"On the singular σk-Yamabe problem"

We prove the existence of constant positive
σk- scalar
curvature
metrics which are complete and conformal to the standard metric on Sn\Λ, where
Λ⊂Sn
is a finite number of points with cardinality at least
two, and n, k are positive integers such that 2 ≤ 2k < n. In general
this problem is equivalent to solve a singular fully nonlinear second
order elliptic equation. For k = 1 (i.e., in the case of the ordinary
scalar curvature) the problem reduces to solve a semilinear elliptic
equation and it has been studied by several authors (Schoen,
Mazzeo-Pacard et al.).