Annales Academiĉ Scientiarum Fennicĉ
Mathematica
Volumen 36, 2011, 423-447

CIRCLE PACKING COMPLEX EARTHQUAKES

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

Texas Tech University, Department of Mathematics
Lubbock, Texas 79409, U.S.A.; roger.w.barnard 'at' ttu.edu

Joint Staff Pentagon
Washington, DC 20318, U.S.A.; eric.murphy 'at' js.pentagon.mil

Texas Tech University, Department of Mathematics
Lubbock, Texas 79409, U.S.A.; brock.williams 'at' ttu.edu

Abstract. Thurston developed shearing earthquake maps as transformations in the Teichmüller space of hyperbolic Riemann surfaces, and McMullen expanded these transformations to include grafting earthquake maps on hyperbolic surfaces. Subsequently, the authors defined an extension of these transformations in describing complex earthquake maps on the Teichmüller space of compact tori. In this paper, we develop computational methods for these transformations using the techniques of circle packing.

2010 Mathematics Subject Classification: Primary 30F60, 52C26.

Key words: Circle packing, conformal maps, Teichmüller theory.

Reference to this article: R.W. Barnard, E.M. Murphy and G.B. Williams: Circle packing complex earthquakes. Ann. Acad. Sci. Fenn. Math. 36 (2011), 423-447.

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doi:10.5186/aasfm.2011.3629

Copyright © 2011 by Academia Scientiarum Fennica