Uniformization of compact foliated spaces by surfaces of hyperbolic type
arXiv:2103.10880
Abstract
We give a new proof of the uniformization theorem of the leaves of a lamination by surfaces of hyperbolic conformal type. We use a laminated version of the Ricci flow to prove the existence of a laminated Riemannian metric (smooth on the leaves, transversaly continuous) with leaves of constant Gaussian curvature equal to -1, which is conformally equivalent to the original metric.
15 pages; Section 5 was rewritten to make more comprehensible the proof of Theorem 5.1.;submitted to Proc. Am. Math. Soc