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Licensed Unlicensed Requires Authentication Published by De Gruyter April 8, 2011

Sets resilient to erosion

Wesley Pegden
From the journal


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.

Received: 2008-06-28
Revised: 2009-03-11
Published Online: 2011-04-08
Published in Print: 2011-April

© de Gruyter 2011

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