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Advances in Geometry

Managing Editor: Grundhöfer, Theo / Joswig, Michael

Editorial Board Member: Bannai, Eiichi / Coskun, Izzet / Duzaar, Frank / Eberlein, Patrick / Gentili, Graziano / Henk, Martin / Kantor, William M. / Korchmaros, Gabor / Kreuzer, Alexander / Lagarias, Jeffrey C. / Leistner, Thomas / Löwen, Rainer / Ono, Kaoru / Pasini, Antonio / Ratcliffe, John G. / Scharlau, Rudolf / Scheiderer, Claus / Van Maldeghem, Hendrik / Weintraub, Steven H. / Weiss, Richard

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1615-7168
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Volume 11, Issue 2 (Jan 2011)

Issues

Sets resilient to erosion

Wesley Pegden
Published Online: 2011-04-08 | DOI: https://doi.org/10.1515/advgeom.2011.002

Abstract

The erosion of a set X in Euclidean space by a radius r > 0 is the subset of X consisting of points at distance ≥ r from the complement of X. A set is resilient to erosion if it is similar to its erosion by some positive radius. We give a somewhat surprising characterization of resilient sets, consisting in one part of simple geometric constraints on convex resilient sets, and, in another, a correspondence between nonconvex resilient sets and scale-invariant (e.g., ‘exact fractal’) sets.

About the article

Received: 2008-06-28

Revised: 2009-03-11

Published Online: 2011-04-08

Published in Print: 2011-04-01


Citation Information: Advances in Geometry, ISSN (Online) 1615-7168, ISSN (Print) 1615-715X, DOI: https://doi.org/10.1515/advgeom.2011.002.

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