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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

Solving Beltrami equations by circle packing


Author: Zheng-Xu He
Journal: Trans. Amer. Math. Soc. 322 (1990), 657-670
MSC: Primary 30C62; Secondary 30C35, 52C15
MathSciNet review: 974518
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Abstract: We use Andreev-Thurston's theorem on the existence of circle packings to construct approximating solutions to the Beltrami equations on Riemann surfaces. The convergence of the approximating solutions on compact subsets will be shown. This gives a constructive proof of the existence theorem for Beltrami equations.


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DOI: http://dx.doi.org/10.1090/S0002-9947-1990-0974518-5
PII: S 0002-9947(1990)0974518-5
Keywords: Circle packing, quasiconformal mapping, Beltrami equation, PL complex
Article copyright: © Copyright 1990 American Mathematical Society