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Transactions of the American Mathematical Society

Published by the American Mathematical Society since 1900, Transactions of the American Mathematical Society is devoted to longer research articles in all areas of pure and applied mathematics.

ISSN 1088-6850 (online) ISSN 0002-9947 (print)

The 2020 MCQ for Transactions of the American Mathematical Society is 1.48.

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The boundary of iterates in Euclidean growth models
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by Janko Gravner PDF
Trans. Amer. Math. Soc. 348 (1996), 4549-4559 Request permission

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.
References
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Additional Information
  • Janko Gravner
  • Affiliation: Department of Mathematics, University of California, Davis, California 95616
  • Email: gravner@feller.ucdavis.edu
  • 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 1996 American Mathematical Society
  • Journal: Trans. Amer. Math. Soc. 348 (1996), 4549-4559
  • MSC (1991): Primary 52A10; Secondary 52A99, 60K35
  • DOI: https://doi.org/10.1090/S0002-9947-96-01697-2
  • MathSciNet review: 1370643