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Solutions to the Singular σ2-Yamabe Problem with Isolated Singularities
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Solutions to the Singular σ2-Yamabe Problem with Isolated Singularities
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Journal Article
Solutions to the Singular σ2-Yamabe Problem with Isolated Singularities
2017
Overview
Given (M,g0) a closed Riemannian manifold and a nonempty closed subset X in M, the singular σk-Yamabe problem asks for a complete metric g on M\\X conformal to g0 with constant σk-curvature. The σk-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 σ2-Yamabe problem with isolated singularities in any nondegenerate closed Riemannian manifold such that the Weyl tensor vanishes to sufficiently high order at the singular points. We will use perturbation techniques and gluing methods.
Publisher
Department of Mathematics of Indiana University
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