On positive solutions to semi-linear conformally invariant equations on locally conformally flat manifolds

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dc.creatorQing, Jie
dc.creatorRaske, David
dc.date2005-09-19
dc.date.accessioned2026-07-07T06:18:11Z
dc.date.available2026-07-07T06:18:11Z
dc.descriptionIn this paper we study the existence and compactness of positive solutions to a family of conformally invariant equations on closed locally conformally flat manifolds. The family of conformally covariant operators $P_α$ were introduced via the scattering theory for Poincaré metrics associated with a conformal manifold $(M^n, [g])$. We prove that, on a closed and locally conformally flat manifold with Poincaré exponent less than $\frac {n-α}2$ for some $α\in [2, n)$, the set of positive smooth solutions to the equation $$ P_αu = u^\frac {n+α}{n-α} $$ is compact in the $C^\infty$ topology. Therefore the existence of positive solutions follows from the existence of Yamabe metrics and a degree theory.
dc.description16 pages
dc.identifierhttps://arxiv.org/abs/math/0509415
dc.identifierhttp://arxiv.org/abs/math/0509415
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/94649
dc.subjectDifferential Geometry
dc.subjectAnalysis of PDEs
dc.subject30F45, 58J50, 35J30
dc.titleOn positive solutions to semi-linear conformally invariant equations on locally conformally flat manifolds
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