@article {2013, title = {Connected Sum Construction for σk-Yamabe Metrics}, journal = {Journal of Geometric Analysis 23, nr.2 (2013), pages 812-854}, number = {arXiv:0910.5353;}, year = {2013}, note = {This article has not yet been published.}, publisher = {Springer}, abstract = {In this paper we produce families of Riemannian metrics with positive constant $\sigma_k$-curvature equal to $2^{-k} {n \choose k}$ by performing the connected sum of two given compact {\em non degenerate} $n$--dimensional solutions $(M_1,g_1)$ and $(M_2,g_2)$ of the (positive) $\sigma_k$-Yamabe problem, provided $2 \leq 2k < n$. The problem is equivalent to solve a second order fully nonlinear elliptic equation.}, doi = {10.1007/s12220-011-9265-1}, url = {http://hdl.handle.net/1963/6441}, author = {Giovanni Catino and Lorenzo Mazzieri} }