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Uniformization of surface laminations. (English) Zbl 0785.57009
Given a compact lamination \(M\) by Riemann surfaces, the existence of a Riemannian metric for which all the leaves have the same constant curvature \(c\) is established provided that the Euler class \(e(M)\) of \(M\) has a fixed sign. That is, \(c<0\) (resp., \(>0\)) iff \(e(M)<0\) (resp., \(>0\)) in the sense that \(\mu(e(M))<0\) (resp., \(>0\)) for any harmonic measure \(\mu\); \(c=0\) iff \(e(M)=0\).

MSC:
57R30 Foliations in differential topology; geometric theory
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