Convex iso-Delaunay regions in strata of translation surfaces

Sam Freedman; Bradley Zykoski

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arXiv · 2509.19550

Convex iso-Delaunay regions in strata of translation surfaces

Sam Freedman·Bradley Zykoski

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Abstract

Strata of translation surfaces are covered by the closures of finitely many iso-Delaunay regions: open subspaces parametrizing surfaces whose Delaunay triangulations are combinatorially equivalent. We prove that the iso-Delaunay regions for triangulations with involutions called triangle matchings are convex with respect to the angle coordinates of the triangles. As a corollary, we show that all iso-Delaunay regions in hyperelliptic stratum components are convex. This work generalizes two directions in the theory of flat surfaces.

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Sam Freedman, Bradley Zykoski. 2025-09-23. Convex iso-Delaunay regions in strata of translation surfaces. https://arxiv.org/abs/2509.19550

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