Work

The inf spectrum of moduli space

Year: 2026

Type: preprint

Abstract: Given a surface of genus $g \geq 2$, its inf spectrum is the ordered multiset of inf lengths of curves on the surface, the infimum being over all hyperbolic metrics. We show that the inf spectrum has exponential growth with coefficients that only depend on g, improving the earlier double exponential upper bound. The proof involves developing a number of tools including the process of "thickening" a surface and the notion of model surfaces. These tools may be of independent interest.

Source: arXiv (Cornell University)

DOI: 10.48550/arxiv.2610.15926

Authors: Basmajian, Ara, Mondal, Sayantika, Parlier, Hugo

Language: English

Topic: Geometric and Algebraic Topology

Subfield: Geometry and Topology

Field: Mathematics

Domain: Physical Sciences

Open Access status: green

Funders: City University of New York, Agence Nationale de la Recherche, Schweizerischer Nationalfonds zur Förderung der Wissenschaftlichen Forschung

Award: Surfaces, Geometry, and Algorithms

OpenAlex ID: W7221791085

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