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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
##### Keywords:
lamination; foliation; Riemann surface; Riemannian metric; curvature
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##### References:
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