%0 Journal Article %J Journal of Geometric Analysis 23, nr.2 (2013), pages 812-854 %D 2013 %T Connected Sum Construction for σk-Yamabe Metrics %A Giovanni Catino %A Lorenzo Mazzieri %X 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. %B Journal of Geometric Analysis 23, nr.2 (2013), pages 812-854 %I Springer %G en %U http://hdl.handle.net/1963/6441 %1 6366 %2 Mathematics %4 -1 %$ Submitted by Maria Pia Calandra (calapia@sissa.it) on 2013-01-29T10:41:53Z No. of bitstreams: 1 0910.5353v2.pdf: 355177 bytes, checksum: 0fa7b4a369607d617c4c167617460165 (MD5) %R 10.1007/s12220-011-9265-1