## International Journal of Differential Equations

- Int. J. Differ. Equ.
- Volume 2012 (2012), Article ID 585298, 6 pages.

### A Measurable Stability Theorem for Holomorphic Foliations Transverse to Fibrations

#### Abstract

We prove that a transversely holomorphic foliation, which is transverse to the fibers of a fibration, is a Seifert fibration if the set of compact leaves is not a zero measure subset. Similarly, we prove that a finitely generated subgroup of holomorphic diffeomorphisms of a connected complex manifold is finite provided that the set of periodic orbits is not a zero measure subset.

#### Article information

**Source**

Int. J. Differ. Equ., Volume 2012 (2012), Article ID 585298, 6 pages.

**Dates**

Received: 22 May 2012

Accepted: 22 July 2012

First available in Project Euclid: 24 January 2017

**Permanent link to this document**

https://projecteuclid.org/euclid.ijde/1485226822

**Digital Object Identifier**

doi:10.1155/2012/585298

**Mathematical Reviews number (MathSciNet)**

MR2959773

**Zentralblatt MATH identifier**

1248.32015

#### Citation

Scardua, Bruno. A Measurable Stability Theorem for Holomorphic Foliations Transverse to Fibrations. Int. J. Differ. Equ. 2012 (2012), Article ID 585298, 6 pages. doi:10.1155/2012/585298. https://projecteuclid.org/euclid.ijde/1485226822