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The boundary of iterates in Euclidean growth models
Author(s):
Janko
Gravner
Journal:
Trans. Amer. Math. Soc.
348
(1996),
4549-4559.
MSC (1991):
Primary 52A10;
Secondary 52A99, 60K35
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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  . 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.
References:
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- J. Gravner, D. Griffeath, Threshold growth dynamics, Trans. Amer. Math. Soc. 340 (1993), 837--870. MR 94b:52006
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Additional Information:
Janko
Gravner
Affiliation:
Department of Mathematics, University of California, Davis, California 95616
Email:
gravner@feller.ucdavis.edu
DOI:
10.1090/S0002-9947-96-01697-2
PII:
S 0002-9947(96)01697-2
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
Copyright of article:
Copyright
1996,
American Mathematical Society
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