# Moduli Spaces of Isoperiodic Forms on Riemann Surfaces

 Title: Moduli Spaces of Isoperiodic Forms on Riemann Surfaces Author: McMullen, Curtis T. Citation: McMullen, Curtis T. 2012. “Moduli Spaces of Isoperiodic Forms on Riemann Surfaces.” Working paper, Department of Mathematics, Harvard University. Full Text & Related Files: mcmullen-isoperiodic-forms.pdf (9.684Mb; PDF) Abstract: This paper describes the intrinsic geometry of a leaf $$\mathcal{A}(L)$$ of the absolute period foliation of the Hodge bundle $$\Omega \bar{M}_g$$: its singular Euclidean structure, its natural foliations and its discretized Teichmuller dynamics. We establish metric completeness of $$\mathcal{A}(L)$$ 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 $$\mathcal{A}(L) \cong \mathbb{H}$$, whose zeros, poles and exotic trajectories are analyzed in detail. Terms of Use: This article is made available under the terms and conditions applicable to Open Access Policy Articles, as set forth at http://nrs.harvard.edu/urn-3:HUL.InstRepos:dash.current.terms-of-use#OAP Citable link to this page: http://nrs.harvard.edu/urn-3:HUL.InstRepos:11880197 Downloads of this work: