Lorenzo Mazzieri (SISSA)
Existence of solutions for the singular $\sigma_k$-Yamabe problem

Abstract: We prove the existence of constant positive $\sigma_k$-curvature
metrics which are complete and conformal to the standard metric on $S^n \
P$, where P is a finite number of symmetrically balanced points of
cardinality at least 2, and n, k are positive integers such that $ 2 \le 2k < n$.
The problem is equivalent to solving a singular fully nonlinear
second order elliptic equation.