A prescribed scalar and boundary mean curvature problem and the Yamabe classification on asymptotically Euclidean manifolds with inner boundary

We consider the problem of finding a metric in a given conformal class with prescribed non-positive scalar curvature and non-positive boundary mean curvature on an asymptotically Euclidean manifold with inner boundary. We obtain a necessary and sufficient condition in terms of a conformal invariant...

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Bibliographic Details
Published in:arXiv.org 2022-04
Main Authors: Sicca, Vladmir, Tsogtgerel, Gantumur
Format: Article
Language:English
Subjects:
Asymptotic properties
Classification
Curvature
Manifolds
Online Access:Get full text
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Summary:We consider the problem of finding a metric in a given conformal class with prescribed non-positive scalar curvature and non-positive boundary mean curvature on an asymptotically Euclidean manifold with inner boundary. We obtain a necessary and sufficient condition in terms of a conformal invariant of the zero sets of the target curvatures for the existence of solutions to the problem and use this result to establish the Yamabe classification of metrics in those manifolds with respect to the solvability of the prescribed curvature problem.
ISSN:2331-8422
DOI:10.48550/arxiv.2204.01002