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Journal Article

Connected sum construction for sigma (k)-Yamabe metrics

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Mazzieri,  Lorenzo
Geometric Analysis and Gravitation, AEI-Golm, MPI for Gravitational Physics, Max Planck Society;

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Citation

Catino, G., & Mazzieri, L. (2013). Connected sum construction for sigma (k)-Yamabe metrics. Journal of Geometric Analysis, 23(2), 709-763.


Cite as: https://hdl.handle.net/11858/00-001M-0000-0015-1918-0
Abstract
In this paper we produce families of Riemannian metrics with positive constant sigmak-curvature equal to 2−k(nk) by performing the connected sum of two given compact non degenerate n--dimensional solutions (M1,g1) and (M2,g2) of the (positive) sigmak-Yamabe problem, provided 2<=2k<n. The problem is equivalent to solve a second order fully nonlinear elliptic equation.