A variational proof for the existence of a conformal metric with preassigned negative Gaussian curvature for compact Riemann surfaces of genus $>1$

dc.creatorDey, Rukmini
dc.date2001-12-19
dc.date2006-05-09
dc.date.accessioned2026-07-07T06:35:27Z
dc.date.available2026-07-07T06:35:27Z
dc.descriptionGiven an smooth function $K <0$ we prove a result by Berger, Kazhdan and others that in every conformal class there exists a metric which attains this function as its Gaussian curvature for a compact Riemann surface of genus $g>1$. We do so by minimizing an appropriate functional using elementary analysis. In particular for $K$ a negative constant, this provides an elementary proof of the uniformization theorem for compact Riemann surfaces of genus $g >1$.
dc.description9 pages, AMS-LaTeX
dc.identifierhttps://arxiv.org/abs/math/0112203
dc.identifierhttp://arxiv.org/abs/math/0112203
dc.identifierCorrected Version to: Proc. Ind. Academy of Sciences, 111 (2001), 407
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/99799
dc.subjectDifferential Geometry
dc.titleA variational proof for the existence of a conformal metric with preassigned negative Gaussian curvature for compact Riemann surfaces of genus $>1$
dc.typetext

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