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Fractional conformal
Laplacians and fractional Yamabe problems
María del Mar González and Jie Qing |
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Vol. 6 (2013), No. 7, 1535–1576
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Abstract |
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Based on the relations between scattering operators of asymptotically hyperbolic metrics and Dirichlet-to-Neumann operators of uniformly degenerate elliptic boundary value problems observed by Chang and González, we formulate fractional Yamabe problems that include the boundary Yamabe problem studied by Escobar. We observe an interesting Hopf-type maximum principle together with interplay between analysis of weighted trace Sobolev inequalities and conformal structure of the underlying manifolds, which extends the phenomena displayed in the classic Yamabe problem and boundary Yamabe problem. |
Keywords
fractional Laplacian, conformal geometry, Yamabe problem
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Mathematical Subject Classification 2010
Primary: 35J70, 53A30, 35R11
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Milestones
Received: 18 September 2011
Revised: 5 September 2012
Accepted: 18 October 2012
Published: 27 December 2013
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Authors |
| María del Mar González | |
| ETSEIB, Departament de Matemàtica
Aplicada I Universitat Politècnica de Catalunya Av. Diagonal, 647 08028 Barcelona Spain |
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| Jie Qing | |
| Department of Mathematics University of California, Santa Cruz 4111 McHenry Santa Cruz, CA 95064 United States |
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