PreprintCC BY 4.0arXiv
Geometric structures, orbit closures and invariant measures in moduli spaces
Abstract
Building on the seminal work of Eskin, Mirzakhani and Mohammadi in the context of dynamics on moduli spaces, we introduce linear loci and linear measures to provide a relatively basic description of orbit closures and invariant measures in strata of translation surfaces. We use this to discuss geometrical properties of orbit closures and invariant measures from the perspective of geometric structures.
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BibTeX
@misc{smillie2026geometric,
title = {{Geometric structures, orbit closures and invariant measures in moduli spaces}},
author = {John Smillie and Florent Ygouf},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.36893},
eprint = {2610.36893},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.36893},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Geometric structures, orbit closures and invariant measures in moduli spaces
AU - John Smillie
AU - Florent Ygouf
PY - 2026
DA - 2026/10/27
PB - arXiv
DO - 10.48550/arxiv.2610.36893
UR - https://arxiv.org/abs/2610.36893
AB - Building on the seminal work of Eskin, Mirzakhani and Mohammadi in the context of dynamics on moduli spaces, we introduce linear loci and linear measures to provide a relatively basic description of orbit closures and invariant measures in strata of translation surfaces. We use this to discuss geometrical properties of orbit closures and invariant measures from the perspective of geometric structures.
ER -