Translator Disclaimer
1 October 2017 Complex projective structures: Lyapunov exponent, degree, and harmonic measure
Bertrand Deroin, Romain Dujardin
Duke Math. J. 166(14): 2643-2695 (1 October 2017). DOI: 10.1215/00127094-2017-0012

Abstract

We study several new invariants associated to a holomorphic projective structure on a Riemann surface of finite analytic type: the Lyapunov exponent of its holonomy which is of probabilistic/dynamical nature and was introduced in our previous work; the degree which measures the asymptotic covering rate of the developing map; and a family of harmonic measures on the Riemann sphere, previously introduced by Hussenot. We show that the degree and the Lyapunov exponent are related by a simple formula and give estimates for the Hausdorff dimension of the harmonic measures in terms of the Lyapunov exponent. In accordance with the famous Sullivan dictionary, this leads to a description of the space of such projective structures that is reminiscent of that of the space of polynomials in holomorphic dynamics.

Citation

Download Citation

Bertrand Deroin. Romain Dujardin. "Complex projective structures: Lyapunov exponent, degree, and harmonic measure." Duke Math. J. 166 (14) 2643 - 2695, 1 October 2017. https://doi.org/10.1215/00127094-2017-0012

Information

Received: 21 July 2015; Revised: 17 February 2017; Published: 1 October 2017
First available in Project Euclid: 26 August 2017

zbMATH: 1381.57013
MathSciNet: MR3707286
Digital Object Identifier: 10.1215/00127094-2017-0012

Subjects:
Primary: 57M50
Secondary: 30C85, 30D35, 30F40, 30F50, 37H15

Rights: Copyright © 2017 Duke University Press

JOURNAL ARTICLE
53 PAGES

This article is only available to subscribers.
It is not available for individual sale.
+ SAVE TO MY LIBRARY

SHARE
Vol.166 • No. 14 • 1 October 2017
Back to Top