Length spectra of flat metrics coming from q-differentials

Marissa Loving

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arXiv · 1810.01793

Length spectra of flat metrics coming from q-differentials

Marissa Loving

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Abstract

When geometric structures on surfaces are determined by the lengths of curves, it is natural to ask: which curves' lengths do we really need to know? It is a result of Duchin--Leininger--Rafi that any flat metric induced by a unit-norm quadratic differential is determined by its marked simple length spectrum. We generalize the notion of simple curves to that of q-simple curves, for any positive integer q, and show that the lengths of q-simple curves suffice to determine a non-positively curved Euclidean cone metric induced by a q-differential.

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Marissa Loving. 2018-10-03. Length spectra of flat metrics coming from q-differentials. https://arxiv.org/abs/1810.01793

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