The Anti-de Sitter Proof of Thurston’s Earthquake Theorem

Diaf, Farid; Seppi, Andrea

doi:10.1007/978-3-031-43502-7_4

In the Tradition of Thurston III 2024

DOI: 10.1007/978-3-031-43502-7_4

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The Anti-de Sitter Proof of Thurston’s Earthquake Theorem

Farid Diaf,

Andrea Seppi

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2024

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The infinitesimal earthquake theorem for vector fields on the circle

Diaf

2024

Trans. Amer. Math. Soc.

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We prove that any continuous vector field on a circle is the extension in a suitable sense, of a unique infinitesimal earthquake of the hyperbolic plane. Furthermore, we obtain other extension results when the vector field is assumed only to be upper or lower semicontinuous. This leads to a generalization of Kerckhoff’s and Gardiner’s infinitesimal earthquake theorems to a broader setting, using a completely novel approach. The proof is based on the geometry of the dual of Minkowski three-space, also called Half-pipe three-geometry. In this way, we obtain a simple characterization of Zygmund vector fields on the circle in terms of width of convex hulls.

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The infinitesimal earthquake theorem for vector fields on the circle

Diaf

2024

Trans. Amer. Math. Soc.

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The Anti-de Sitter Proof of Thurston’s Earthquake Theorem

Cited by 1 publication

References 16 publications

The infinitesimal earthquake theorem for vector fields on the circle

The infinitesimal earthquake theorem for vector fields on the circle

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