Deformations on tori

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2006-05

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Abstract

Deformations of Riemann surfaces have been studied for some time. The prominent deformation actions along surfaces are conformal weldings and the earthquake maps developed by William Thurston and Curtis McMullen. Previously, these deformations have required that a surface be cut open along a geodesic. We describe actions similar to conformal weldings and earthquakes in which cutting along a geodesic is not required. In particular, we explore the results of cutting a compact, Euclidean Riemann surface along a circle and applying similar actions. Using the discrete conformal approximations of circle packing, we describe a method by which these actions can be numerically estimated.

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Deformations

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