Constant $\sigma_{k}$-curvature metrics with Delaunay type ends

Lorenzo Mazzieri; Antonio Segatti

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arXiv · 1008.0490

Constant $\sigma_{k}$-curvature metrics with Delaunay type ends

Lorenzo Mazzieri·Antonio Segatti

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Abstract

In this paper we produce families of complete non compact Riemannian metrics with positive constant $\sigma_k$-curvature by performing the connected sum of a finite number of given $n$-dimensional Delaunay type solutions, provided $2 \leq 2k < n$. The problem is equivalent to solve a second order fully nonlinear elliptic equation.

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Lorenzo Mazzieri, Antonio Segatti. 2010-08-03. Constant $\sigma_{k}$-curvature metrics with Delaunay type ends. https://arxiv.org/abs/1008.0490

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