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}
}
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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