Israel Journal of Mathematics

, Volume 130, Issue 1, pp 323–346

Curvature and uniformization


    • Department of MathematicsStanford University
  • Michael Taylor
    • Department of MathematicsUniversity of North Carolina

DOI: 10.1007/BF02764082

Cite this article as:
Mazzeo, R. & Taylor, M. Isr. J. Math. (2002) 130: 323. doi:10.1007/BF02764082


We 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-e2u=Ko(z) on general open surfaces. A few other topics are discussed, including boundary behavior of the conformal factore2u giving the Poincaré metric when the Riemann surface has smoothly bounded compact closure, and also a curvature equation proof of Koebe's disk theorem.

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© Hebrew University 2002