English

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