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arXiv · 2607.24181

Hausdorff dimension of non-uniquely ergodic directions in eigenform loci

Yuming Wei·Pengyu Yang
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Abstract

We consider the eigenform locus $\mathcal{E}_D$ in $\mathcal{H}(1,1)$ where $D$ is not a square. We prove that for any translation surface $(X,\omega) \in \mathcal{E}_D$, the set of non-uniquely ergodic directions has Hausdorff dimension $1/2$, except when $D=5$ and $(X,\omega)$ lies in the Teichm\"uller curve generated by the regular decagon.

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Yuming Wei, Pengyu Yang. 2026-07-27. Hausdorff dimension of non-uniquely ergodic directions in eigenform loci. https://arxiv.org/abs/2607.24181

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