Can You Hear the Shape of a Hyperbolic Surface? Now for Real
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arXiv
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| Format: | Preprint |
| Published: |
2026
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| _version_ | 1866917462997467136 |
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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 |