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

Fernando C. Marques

doi:10.4310/CAG.2007.v15.n2.a7

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

Fernando C. Marques

Research output: Contribution to journal › Article › peer-review

56 Scopus citations

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.

Original language	English (US)
Pages (from-to)	381-405
Number of pages	25
Journal	Communications in Analysis and Geometry
Volume	15
Issue number	2
DOIs	https://doi.org/10.4310/CAG.2007.v15.n2.a7
State	Published - Mar 2007
Externally published	Yes

All Science Journal Classification (ASJC) codes

Analysis
Statistics and Probability
Geometry and Topology
Statistics, Probability and Uncertainty

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10.4310/CAG.2007.v15.n2.a7

Cite this

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AB - 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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ER -

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

Abstract

All Science Journal Classification (ASJC) codes

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