Shortest filling geodesics on hyperbolic surfaces

Published 14 Jun 2025 in math.GT | (2506.12465v1)

Abstract: In this paper, we obtain the minimal length of a filling (multi-)geodesic on a genus $g$ hyperbolic surface in the moduli space of hyperbolic surfaces and show that it is realized by the geodesic whose complement is a right-angled regular $(8g-4)$ -gon. A single geodesic realizing this minimum is provided.

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