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The shapes of complementary subsurfaces to simple closed hyperbolic multi-geodesics.

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Titel: The shapes of complementary subsurfaces to simple closed hyperbolic multi-geodesics.
Autoren: Arana–Herrera, Francisco1 (AUTHOR) farana@umd.edu, Calderon, Aaron2 (AUTHOR) aaroncalderon@uchicago.edu
Quelle: Inventiones Mathematicae. Nov2025, Vol. 242 Issue 2, p571-626. 56p.
Schlagwörter: *HYPERBOLIC geometry, *MODULI theory, *GEODESICS, *GEOMETRIC measure theory
Abstract: Cutting a hyperbolic surface X along a simple closed multi-geodesic results in a hyperbolic structure on the complementary subsurface. We study the distribution of the shapes of these subsurfaces in moduli space as boundary lengths go to infinity, showing that they equidistribute to the Kontsevich measure on a corresponding moduli space of metric ribbon graphs. In particular, random subsurfaces look like random ribbon graphs, a law which does not depend on the initial choice of X . This result strengthens Mirzakhani's famous simple closed multi-geodesic counting theorems for hyperbolic surfaces. [ABSTRACT FROM AUTHOR]
Datenbank: Academic Search Index
Beschreibung
Abstract:Cutting a hyperbolic surface X along a simple closed multi-geodesic results in a hyperbolic structure on the complementary subsurface. We study the distribution of the shapes of these subsurfaces in moduli space as boundary lengths go to infinity, showing that they equidistribute to the Kontsevich measure on a corresponding moduli space of metric ribbon graphs. In particular, random subsurfaces look like random ribbon graphs, a law which does not depend on the initial choice of X . This result strengthens Mirzakhani's famous simple closed multi-geodesic counting theorems for hyperbolic surfaces. [ABSTRACT FROM AUTHOR]
ISSN:00209910
DOI:10.1007/s00222-025-01364-7