Can You Hear the Shape of a Hyperbolic Surface? Now for Real

Fuente: arXiv
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Main Authors: Battista, Ludovico, Souto, Juan
Format: Preprint
Published: 2026
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author Battista, Ludovico
Souto, Juan
author_facet Battista, Ludovico
Souto, Juan
contents We associate a musical instrument, a "hyperbolic marimba", to every pair $(X,Γ)$ where $X$ is a hyperbolic surface and $Γ\subset X$ a simple multicurve labeled with musical keys. It works as follows: take a geodesic and every time it hits $Γ$, play the corresponding note. In this paper we investigate to which extent the so-produced melodies characterize $(X,Γ)$ up to isometry. In the accompanying website "HyperMarimba" (available at https://ludox73.github.io/HyperMarimba/story.html ), the reader can actually listen to the produced melodies. They can also visualize some of the phenomena we investigate.
format Preprint
id arxiv_https___arxiv_org_abs_2604_27990
institution arXiv
publishDate 2026
record_format arxiv
spellingShingle Can You Hear the Shape of a Hyperbolic Surface? Now for Real
Battista, Ludovico
Souto, Juan
Differential Geometry
Dynamical Systems
Geometric Topology
We associate a musical instrument, a "hyperbolic marimba", to every pair $(X,Γ)$ where $X$ is a hyperbolic surface and $Γ\subset X$ a simple multicurve labeled with musical keys. It works as follows: take a geodesic and every time it hits $Γ$, play the corresponding note. In this paper we investigate to which extent the so-produced melodies characterize $(X,Γ)$ up to isometry. In the accompanying website "HyperMarimba" (available at https://ludox73.github.io/HyperMarimba/story.html ), the reader can actually listen to the produced melodies. They can also visualize some of the phenomena we investigate.
title Can You Hear the Shape of a Hyperbolic Surface? Now for Real
topic Differential Geometry
Dynamical Systems
Geometric Topology
url https://arxiv.org/abs/2604.27990