Uniformization of compact foliated spaces by surfaces of hyperbolic type
Differential Geometry
2021-08-05 v3
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.
Keywords
Cite
@article{arxiv.2103.10880,
title = {Uniformization of compact foliated spaces by surfaces of hyperbolic type},
author = {Richard Muñiz and Alberto Verjovsky},
journal= {arXiv preprint arXiv:2103.10880},
year = {2021}
}
Comments
15 pages; Section 5 was rewritten to make more comprehensible the proof of Theorem 5.1.;submitted to Proc. Am. Math. Soc