Connected sum construction for $\sigma_k$-Yamabe metrics

Giovanni Catino; Lorenzo Mazzieri

Connected sum construction for $\sigma_k$-Yamabe metrics

Differential Geometry 2014-10-10 v2 Analysis of PDEs

Authors: Giovanni Catino , Lorenzo Mazzieri

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.

Keywords

yamabe problem

Cite

@article{arxiv.0910.5353,
  title  = {Connected sum construction for $\sigma_k$-Yamabe metrics},
  author = {Giovanni Catino and Lorenzo Mazzieri},
  journal= {arXiv preprint arXiv:0910.5353},
  year   = {2014}
}

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