# Connected sum construction for sigma$_k$-Yamabe metrics

created by catino on 30 Oct 2009
modified on 28 Feb 2013

[BibTeX]

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.