Euclidean earthquakes

Roger W. Barnard; Eric M. Murphy; G. Brock Williams

doi:10.1080/17476930902763793

Euclidean earthquakes

Roger W. Barnard, Eric M. Murphy, G. Brock Williams

Mathematics and Statistics

Research output: Contribution to journal › Article › peer-review

1 Scopus citations

Abstract

William Thurston developed shearing earthquake maps as transformations in the Teichmüller space of hyperbolic Riemann surfaces, and Curtis McMullen expanded these transformations to include grafting earthquake maps on hyperbolic surfaces. These earthquake maps have been extensively studied, but the literature is confined to earthquake transformations on hyperbolic surfaces. In this article, we define similar transformations on the Teichmüller space of compact tori and describe the differences between the hyperbolic and Euclidean earthquakes.

Original language	English
Pages (from-to)	639-652
Number of pages	14
Journal	Complex Variables and Elliptic Equations
Volume	54
Issue number	7
DOIs	https://doi.org/10.1080/17476930902763793
State	Published - Jul 2009

Keywords

Riemann surface
Teichmuller theory

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10.1080/17476930902763793

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title = "Euclidean earthquakes",

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AU - Williams, G. Brock

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AB - William Thurston developed shearing earthquake maps as transformations in the Teichmüller space of hyperbolic Riemann surfaces, and Curtis McMullen expanded these transformations to include grafting earthquake maps on hyperbolic surfaces. These earthquake maps have been extensively studied, but the literature is confined to earthquake transformations on hyperbolic surfaces. In this article, we define similar transformations on the Teichmüller space of compact tori and describe the differences between the hyperbolic and Euclidean earthquakes.

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KW - Teichmuller theory

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