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Mathematics > Differential Geometry

arXiv:1507.00053 (math)
[Submitted on 30 Jun 2015]

Title:Solutions to the singular $σ_2-$Yamabe problem with isolated singularities

Authors: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.
Comments: 35 pages. arXiv admin note: text overlap with arXiv:0911.4477
Subjects: Differential Geometry (math.DG)
MSC classes: 53C21, 53A30
Cite as: arXiv:1507.00053 [math.DG]
  (or arXiv:1507.00053v1 [math.DG] for this version)
  https://doi.org/10.48550/arXiv.1507.00053

Submission history

From: Almir Silva Santos [view email]
[v1] Tue, 30 Jun 2015 22:28:51 UTC (31 KB)
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