On a geometric equation with critical nonlinearity on the boundary

dc.creatorFelli, Veronica
dc.creatorAhmedou, Mohameden Ould
dc.date2001-06-26
dc.date2002-05-22
dc.date.accessioned2026-07-07T04:42:19Z
dc.date.available2026-07-07T04:42:19Z
dc.descriptionA theorem of Escobar asserts that, on a positive three dimensional smooth compact Riemannian manifold with boundary which is not conformally equivalent to the standard three dimensional ball, a necessary and sufficient condition for a $C^2$ function $H$ to be the mean curvature of some conformal flat metric is that $H$ is positive somewhere. We show that, when the boundary is umbilic and the function $H$ is positive everywhere, all such metrics stay in a compact set with respect to the $C^2$ norm and the total degree of all solutions is equal to -1.
dc.description28 pages
dc.identifierhttps://arxiv.org/abs/math/0106219
dc.identifierhttp://arxiv.org/abs/math/0106219
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/61732
dc.subjectAnalysis of PDEs
dc.subjectDifferential Geometry
dc.subject35J60, 53C21, 58G30
dc.titleOn a geometric equation with critical nonlinearity on the boundary
dc.typetext

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