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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Oblatum 3-III-1999 & 18-II-2000¶Published online: 8 May 2000
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Chang, SY., Qing, J. & Yang, P. Compactification of a class of conformally flat 4-manifold. Invent. math. 142, 65–93 (2000). https://doi.org/10.1007/s002220000083
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DOI: https://doi.org/10.1007/s002220000083