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arXiv · 2608.20264

Systole Increasing Deformations to Maximal Translation Surfaces

Achintya Dey·Bidyut Sanki
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Abstract

A unit-area translation surface is called \emph{maximal} if it maximizes the length of the shortest saddle connection among all surfaces in the same stratum. We investigate whether a non-maximal translation surface can be continuously deformed into a maximal one while the systole increases strictly monotonically. Although such a deformation does not exist in general due to the existence of local but not global maxima of the systole function, we prove that it exists for square-tiled surfaces and translation surfaces obtained from regular hexagons and regular octagons. In each case, we explicitly construct a continuous deformation to a maximal translation surface along which the systole is strictly increasing. Finally, the preceding construction yields another family of translation surfaces admitting continuous systole-increasing deformations to maximal surfaces.

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BibTeXRIS

Achintya Dey, Bidyut Sanki. 2026-08-20. Systole Increasing Deformations to Maximal Translation Surfaces. https://arxiv.org/abs/2608.20264

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