Yamabe classification and prescribed scalar curvature in the asymptotically Euclidean setting
| Autor: | James Dilts, David Maxwell |
|---|---|
| Rok vydání: | 2018 |
| Předmět: |
Mathematics - Differential Geometry
Statistics and Probability Pure mathematics Conformal map 53C20 01 natural sciences Mathematics - Analysis of PDEs 0103 physical sciences FOS: Mathematics Compactification (mathematics) 0101 mathematics Mathematics Zero set 010308 nuclear & particles physics 010102 general mathematics Manifold Differential Geometry (math.DG) Mathematics::Differential Geometry Geometry and Topology Statistics Probability and Uncertainty Laplace operator Analysis Analysis of PDEs (math.AP) Scalar curvature Sign (mathematics) Yamabe invariant |
| Zdroj: | Communications in Analysis and Geometry. 26:1127-1168 |
| ISSN: | 1944-9992 1019-8385 |
| DOI: | 10.4310/cag.2018.v26.n5.a5 |
| Popis: | We prove a necessary and sufficient condition for an asymptotically Euclidean manifold to be conformally related to one with specified nonpositive scalar curvature: the zero set of the desired scalar curvature must have a positive Yamabe invariant, as defined in the article. We show additionally how the sign of the Yamabe invariant of a measurable set can be computed from the sign of certain generalized "weighted" eigenvalues of the conformal Laplacian. Using the prescribed scalar curvature result we give a characterization of the Yamabe classes of asymptotically Euclidean manifolds. We also show that the Yamabe class of an asymptotically Euclidean manifold is the same as the Yamabe class of its conformal compactification. 30 pages |
| Databáze: | OpenAIRE |
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