A Compactness Theorem for Embedded Measured Riemann Surface Laminations

Divakaran Divakaran; Dheeraj Kulkarni

A Compactness Theorem for Embedded Measured Riemann Surface Laminations

Geometric Topology 2018-01-04 v2 Complex Variables Dynamical Systems

Authors: Divakaran Divakaran , Dheeraj Kulkarni

Abstract

We prove a compactness theorem for embedded measured hyperbolic Riemann surface laminations in a compact almost complex manifold $(X, J)$ . To prove compactness result, we show that there is a suitable topology on the space of measured Riemann surface laminations induced by Levy-Prokhorov metric. As an application of the compactness theorem, we show that given a biholomorphism of $\phi$ of a closed complex manifold $X$ , some power $\phi^k$ ( $k>0$ ) fixes a measured Riemann surface lamination in $X$ .

Keywords

isometric immersions riemannian geometry metric embeddings

Cite

@article{arxiv.1610.01770,
  title  = {A Compactness Theorem for Embedded Measured Riemann Surface Laminations},
  author = {Divakaran Divakaran and Dheeraj Kulkarni},
  journal= {arXiv preprint arXiv:1610.01770},
  year   = {2018}
}

Comments

Error in the proof of the main theorem. The error can not be fixed

A Compactness Theorem for Embedded Measured Riemann Surface Laminations

Abstract

Keywords

Cite

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