• A complete conformal metric of preassigned negative Gaussian curvature for a punctured hyperbolic Riemann surface

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    • Keywords


      Punctured Riemann surfaces; prescribed curvature

    • Abstract


      Leth be a complete metric of Gaussian curvature K0 on a punctured Riemann surface of genusg ≥ 1 (or the sphere with at least three punctures). Given a smooth negative functionK withK =K0 in neighbourhoods of the punctures we prove that there exists a metric conformal toh which attains this function as its Gaussian curvature for the punctured Riemann surface. We do so by minimizing an appropriate functional using elementary analysis.

    • Author Affiliations


      Rukmini Dey1

      1. Department of Mathematics, Indian Institute of Technology, Kanpur - 208 016, India
    • Dates

  • Proceedings – Mathematical Sciences | News

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      Posted on July 25, 2019

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