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arXiv · 2510.18128

Cohomological equation for geodesic flows on flat surfaces

Giovanni Forni·Nelson Moll
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Abstract

We prove the existence of solutions of the cohomological equation for the geodesic flow on the unit tangent bundle of a compact flat surface with finitely many cone points. We also prove the ergodicity of the holonomy foliation for surfaces with non-rational holonomy, and the cohomology-free property of the horizontal foliated Laplacian under a simultaneous Diophantine condition.

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Giovanni Forni, Nelson Moll. 2025-10-20. Cohomological equation for geodesic flows on flat surfaces. https://arxiv.org/abs/2510.18128

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