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Connected Sum Construction for σk-Yamabe Metrics

TitleConnected Sum Construction for σk-Yamabe Metrics
Publication TypeJournal Article
Year of Publication2013
AuthorsCatino, G, Mazzieri, L
JournalJournal of Geometric Analysis 23, nr.2 (2013), pages 812-854

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.

Alternate JournalConnected Sum Contruction for GammaK-Yamabe Metrics

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