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arXiv · 1507.00053

Solutions to the singular $\sigma_2-$Yamabe problem with isolated singularities

Almir Silva Santos
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Abstract

Given $(M,g_0)$ a closed Riemannian manifold and a nonempty closed subset $X$ in $M$, the singular $\sigma_k-$Yamabe problem asks for a complete metric $g$ on $M\backslash X$ conformal to $g_0$ with constant $\sigma_k-$curvature. The $\sigma_k-$curvature is defined as the $k-$th elementary symmetric function of the eigenvalues of the Schouten tensor of a Riemannian metric. The main goal of this paper is to find solutions to the singular $\sigma_2-$Yamabe problem with isolated singularities in any compact non-degenerate manifold such that the Weyl tensor vanishing to sufficiently high order at the singular point. We will use perturbation techniques and gluing methods.

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Almir Silva Santos. 2015-06-30. Solutions to the singular $\sigma_2-$Yamabe problem with isolated singularities. https://arxiv.org/abs/1507.00053

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