Existence results for the Yamabe problem on manifolds with boundary

Fernando Coda Santos Cavalcanti Marques

doi:10.1512/iumj.2005.54.2590

Existence results for the Yamabe problem on manifolds with boundary

Fernando Coda Santos Cavalcanti Marques

Research output: Contribution to journal › Review article › peer-review

74 Scopus citations

Abstract

Given a compact Riemannian manifold with umbilic boundary, we prove the existence of conformally related metrics of zero scalar curvature and constant mean curvature on the boundary, under suitable hypotheses on the Weyl tensor. In order to carry out the estimates on the Sobolev quotient, we also prove the existence of conformal Fermi coordinates.

Original language	English (US)
Pages (from-to)	1599-1620
Number of pages	22
Journal	Indiana University Mathematics Journal
Volume	54
Issue number	6
DOIs	https://doi.org/10.1512/iumj.2005.54.2590
State	Published - Jan 1 2005
Externally published	Yes

All Science Journal Classification (ASJC) codes

Mathematics(all)

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10.1512/iumj.2005.54.2590

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title = "Existence results for the Yamabe problem on manifolds with boundary",

abstract = "Given a compact Riemannian manifold with umbilic boundary, we prove the existence of conformally related metrics of zero scalar curvature and constant mean curvature on the boundary, under suitable hypotheses on the Weyl tensor. In order to carry out the estimates on the Sobolev quotient, we also prove the existence of conformal Fermi coordinates.",

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AB - Given a compact Riemannian manifold with umbilic boundary, we prove the existence of conformally related metrics of zero scalar curvature and constant mean curvature on the boundary, under suitable hypotheses on the Weyl tensor. In order to carry out the estimates on the Sobolev quotient, we also prove the existence of conformal Fermi coordinates.

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DO - 10.1512/iumj.2005.54.2590

M3 - Review article

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JO - Indiana University Mathematics Journal

JF - Indiana University Mathematics Journal

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Existence results for the Yamabe problem on manifolds with boundary

Abstract

All Science Journal Classification (ASJC) codes

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