Curvature and Uniformization

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dc.creatorMazzeo, Rafe
dc.creatorTaylor, Michael
dc.date2001-05-02
dc.date.accessioned2026-07-07T04:41:34Z
dc.date.available2026-07-07T04:41:34Z
dc.descriptionWe approach the problem of uniformization of general Riemann surfaces through consideration of the curvature equation, and in particular the problem of constructing Poincaré metrics (i.e., complete metrics of constant negative curvature) by solving the equation $Δu - e^{2u} = K_0(z)$ on general open surfaces. A few other topics are discussed, including boundary behavior of the conformal factor $e^{2u}$ giving the Poincaré metric when the Riemann surface has smoothly bounded compact closure, and also a curvature equation proof of Koebe's disk theorem.
dc.description26 pages
dc.identifierhttps://arxiv.org/abs/math/0105016
dc.identifierhttp://arxiv.org/abs/math/0105016
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/61411
dc.subjectDifferential Geometry
dc.subjectAnalysis of PDEs
dc.subject53C07; 30F45
dc.titleCurvature and Uniformization
dc.typetext

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