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Earthquakes and circle packings

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Abstract

We prove that earthquakes on hyperbolic surfaces can be approximated by discrete earthquakes constructed using circle packings. Consequently, we obtain a combinatorial version of Thurston’s Earthquake Theorem. Any surface can be approximated by combinatorial earthquakes of a packable surface. This provides a controlled combinatorial method for deforming hyperbolic surfaces.

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Williams, G.B. Earthquakes and circle packings. J. Anal. Math. 85, 371–396 (2001). https://doi.org/10.1007/BF02788088

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  • DOI: https://doi.org/10.1007/BF02788088

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