Constant ${\sigma }_k$-curvature metrics with Delaunay type ends

Abstract

In this paper we produce families of complete non compact Riemannian metrics with positive constant ${\sigma }_k$-curvature by performing the connected sum of a finite number of given $n$-dimensional Delaunay type solutions, provided $2\le 2k<n$. The problem is equivalent to solve a second order fully nonlinear elliptic equation.