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

DOI:
https://doi.org/10.1090/S0002-9939-01-06243-8

Published electronically:
August 28, 2001

MathSciNet review:
1866036

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Abstract | References | Similar Articles | Additional Information

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:
https://doi.org/10.1090/S0002-9939-01-06243-8

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