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

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      https://www.ias.ac.in/article/fulltext/pmsc/111/04/0407-0414

    • Keywords

       

      Uniformization theorem; Riemann surfaces; prescribed Gaussian curvature

    • Abstract

       

      Given a smooth functionK < 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 genusg > 1. We do so by minimizing an appropriate functional using elementary analysis. In particular forK a negative constant, this provides an elementary proof of the uniformization theorem for compact Riemann surfaces of genusg > 1.

    • Author Affiliations

       

      Rukmini Dey1

      1. Harish Chandra Research Institute, Chhatnag Road, Jhusi, Allahabad - 211 019, India
    • Dates

       
  • Proceedings – Mathematical Sciences | News

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