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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Harmonic mappings of the Sierpinski gasket to the circle


Author: Robert S. Strichartz
Journal: Proc. Amer. Math. Soc. 130 (2002), 805-817
MSC (2000): Primary 28A80, 58E20
Published electronically: August 28, 2001
MathSciNet review: 1866036
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Abstract:

Harmonic mappings from the Sierpinski gasket to the circle are described explicitly in terms of boundary values and topological data. In particular, all such mappings minimize energy within a given homotopy class. Explicit formulas are also given for the energy of the mapping and its normal derivatives at boundary points.


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Additional Information

Robert S. Strichartz
Affiliation: Department of Mathematics, Malott Hall, Cornell University, Ithaca, New York 14853
Email: str@math.cornell.edu

DOI: http://dx.doi.org/10.1090/S0002-9939-01-06243-8
PII: S 0002-9939(01)06243-8
Keywords: Sierpinski gasket, harmonic mappings, analysis on fractals, self--similar Dirichlet form
Received by editor(s): September 15, 2000
Published electronically: August 28, 2001
Additional Notes: This research was supported in part by the National Science Foundation, Grant DMS 9970337
Communicated by: Christopher D. Sogge
Article copyright: © Copyright 2001 American Mathematical Society