# Moduli spaces of isoperiodic forms on Riemann surfaces

@article{McMullen2014ModuliSO, title={Moduli spaces of isoperiodic forms on Riemann surfaces}, author={Curtis T. McMullen}, journal={Duke Mathematical Journal}, year={2014}, volume={163}, pages={2271-2323} }

This paper describes the intrinsic geometry of a leaf A(L) of the absolute period foliation of the Hodge bundle ΩMg: its singular Euclidean structure, its natural foliations and its discretized Teichmüller dynamics. We establish metric completeness of A(L) for general g, and then turn to a study of the case g = 2. In this case the Euclidean structure comes from a canonical meromorphic quadratic differential on A(L) ∼= H, whose zeros, poles and exotic trajectories are analyzed in detail.

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