Inventiones mathematicae

, Volume 142, Issue 1, pp 65–93

Compactification of a class of conformally flat 4-manifold

  • Sun-Yung A. Chang
  • Jie Qing
  • Paul C. Yang

Abstract.

In this paper we generalize Huber’s result on complete surfaces of finite total curvature. For complete locally conformally flat 4-manifolds of positive scalar curvature with Q curvature integrable, where Q is a variant of the Chern-Gauss-Bonnet integrand; we first derive the Cohn-Vossen inequality. We then establish finiteness of the topology. This allows us to provide conformal compactification of such manifolds.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2000

Authors and Affiliations

  • Sun-Yung A. Chang
    • 1
  • Jie Qing
    • 3
  • Paul C. Yang
    • 4
  1. 1.Department of Mathematics, Princeton University, Princeton, NJ 08544, USA¶(e-mail: chang@math.princeton.edu)US
  2. 2.Department of Mathematics, UCLA, Los Angeles, CA 90095, USAUS
  3. 3.Department of Mathematics, University of California, Santa Cruz, Santa Cruz, CA 95064, USA (e-mail: qing@math.ucsc.edu)US
  4. 4.Department of Mathematics, University of Southern California, Los Angeles, CA 90089, USA (e-mail: pyang@math.usc.edu)US

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