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https://hdl.handle.net/1959.11/21451
Title: | The Asymptotically Flat Scalar-Flat Yamabe Problem with Boundary | Contributor(s): | McCormick, Steve (author) | Publication Date: | 2017 | Open Access: | Yes | DOI: | 10.1007/s12220-017-9760-0 | Handle Link: | https://hdl.handle.net/1959.11/21451 | Abstract: | We consider two cases of the asymptotically flat scalar-flat Yamabe problem on a non-compact manifold with inner boundary in dimension n ≥ 3. First, following arguments of Cantor and Brill in the compact case, we show that given an asymptotically flat metric g, there is a conformally equivalent asymptotically flat scalar-flat metric that agrees with g on the boundary. We then replace the metric boundary condition with a condition on the mean curvature: given a function f on the boundary that is not too large, we show that there is an asymptotically flat scalar-flat metric, conformally equivalent to g whose boundary mean curvature is given by f. The latter case involves solving an elliptic PDE with critical exponent using the method of sub- and supersolutions. Both results require the usual assumption that the Sobolev quotient is positive. | Publication Type: | Journal Article | Source of Publication: | Journal of Geometric Analysis, 27(3), p. 2269-2277 | Publisher: | Springer New York LLC | Place of Publication: | United States of America | ISSN: | 1559-002X 1050-6926 |
Fields of Research (FoR) 2008: | 010110 Partial Differential Equations 010102 Algebraic and Differential Geometry |
Fields of Research (FoR) 2020: | 490410 Partial differential equations 490402 Algebraic and differential geometry |
Socio-Economic Objective (SEO) 2008: | 970101 Expanding Knowledge in the Mathematical Sciences | Socio-Economic Objective (SEO) 2020: | 280118 Expanding knowledge in the mathematical sciences | Peer Reviewed: | Yes | HERDC Category Description: | C1 Refereed Article in a Scholarly Journal |
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Appears in Collections: | Journal Article School of Science and Technology |
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