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Annals of Mathematics, II. Series Vol. 149, No. 1, pp. 133 (1999) 

Rigidity of infinite disk patternsZhengXu HeReview from Zentralblatt MATH: Let $P$ be a locally finite disk pattern on the complex plane $\bbfC$ whose combinatorics are described by the oneskelton $G$ of a triangulation of the open topological disk and whose dihedral angles are equal to a function $\theta:E\to[0,\pi/2]$ on the set of edges. The author shows that $P$ is determined up to a euclidean similarity. If $\theta=0$ this was proved earlier by Rodin and Sullivan and generalized by O. Schramm. Their methods do not work here. The author uses new clever ideas including discrete potential theory, probabilistic methods first developed by K. Stephenson, etc. as well as other important tools. Reviewed by Dov Aharonov Keywords: packing of the plane; discrete potential theory; maximum principle; extremal length Classification (MSC2000): 30C99 Full text of the article:
Electronic fulltext finalized on: 18 Aug 2001. This page was last modified: 21 Jan 2002.
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