*Published Paper*

**Inserted:** 30 oct 2009

**Last Updated:** 28 feb 2013

**Journal:** J. Geom. Anal.

**Volume:** 23

**Number:** 2

**Pages:** 812-854

**Year:** 2013

**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 *non degenerate* $n$--dimensional solutions $(M_1,g_1)$ and $(M_2,g_2)$ of the (positive) $sigma_k$-Yamabe problem, provided $2 <= 2k < n$. The problem is equivalent to solve a second order fully nonlinear elliptic equation.

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