# Lower bounds for Lyapunov exponents of flat bundles on curves

```@article{Eskin2016LowerBF,
title={Lower bounds for Lyapunov exponents of flat bundles on curves},
author={A. V. Eskin and Maxim Kontsevich and Martin Moeller and Anton Zorich},
journal={arXiv: Geometric Topology},
year={2016}
}```
• Published 5 September 2016
• Mathematics
• arXiv: Geometric Topology
Consider a flat bundle over a complex curve. We prove a conjecture of Fei Yu that the sum of the top k Lyapunov exponents of the flat bundle is always greater or equal to the degree of any rank k holomorphic subbundle. We generalize the original context from Teichmueller curves to any local system over a curve with non-expanding cusp monodromies. As an application we obtain the large genus limits of individual Lyapunov exponents in hyperelliptic strata of Abelian differentials. Understanding…

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