Finsler metrics on $1/n$-translation structures on surfaces

Beatrice Pozzetti; Jiajun Shi

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arXiv · 2604.02243

Finsler metrics on $1/n$-translation structures on surfaces

Beatrice Pozzetti·Jiajun Shi

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Abstract

We define compatible Finsler distances on $1/n$-translation surfaces, we study their geodesics, and construct a Liouville current for each such metric, that is a geodesic current that encodes the information of the length of the closed curves. The construction is based on multi-foliations, a generalization of measured foliations of independent interest.

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Beatrice Pozzetti, Jiajun Shi. 2026-04-02. Finsler metrics on $1/n$-translation structures on surfaces. https://arxiv.org/abs/2604.02243

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