Conformal deformations to scalar-flat metrics with constant mean curvature on the boundary

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Abstract

Let (Mn,g) be a compact manifold with boundary, with finite Sobolev quotient Q(Mn, ∂M). We prove that there exists a conformal deformation which is scalar-flat and has constant boundary mean curvature, if n = 4 or 5 and the boundary is not umbilic. In particular, we prove such existence for any smooth and bounded open set of the Euclidean space, finishing the remaining cases of a theorem of J.F. Escobar.

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APA

Marques, F. C. (2007). Conformal deformations to scalar-flat metrics with constant mean curvature on the boundary. Communications in Analysis and Geometry, 15(2), 381–405. https://doi.org/10.4310/CAG.2007.v15.n2.a7

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