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Transactions of the American Mathematical Society

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The boundary of iterates in
Euclidean growth models

Author: Janko Gravner
Journal: Trans. Amer. Math. Soc. 348 (1996), 4549-4559
MSC (1991): Primary 52A10; Secondary 52A99, 60K35
MathSciNet review: 1370643
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Abstract: This paper defines a general Euclidean growth model via a translation invariant, monotone and local transformation on Borel subsets of $\mathbf {R}^2$. The main result gives a geometric condition for the boundary curvature of the iterates to go to 0. Consequences include estimates for the speed of convergence to the asymptotic shape, and a result about survival of Euclidean deterministic forest fires.

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Additional Information

Janko Gravner
Affiliation: Department of Mathematics, University of California, Davis, California 95616

Keywords: Growth dynamics, curvature, deterministic forest fire
Received by editor(s): July 14, 1995
Additional Notes: This research was partially supported by the research grant J1-6157-0101-94 from the Republic of Slovenia’s Ministry of Science
Article copyright: © Copyright 1996 American Mathematical Society