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Sets resilient to erosion
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Wesley Pegden
Published/Copyright:
April 8, 2011
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.
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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Articles in the same Issue
- On finite subgroups of compact Lie groups and fundamental groups of Riemannian manifolds
- Sets resilient to erosion
- On duality and endomorphisms of lattices of closed convex sets
- On the complexity group of stable curves
- Isoperimetric inequalities for wave fronts and a generalization of Menzin's conjecture for bicycle monodromy on surfaces of constant curvature
- Character tables of m-flat association schemes
- Character tables of the association schemes obtained from the finite affine classical groups acting on the sets of maximal totally isotropic flats
- Bounds on the roots of the Steiner polynomial
- Polarities of Schellhammer planes
- Substituting compact disks in stable planes
- On the local structure and the homology of CAT(κ) spaces and euclidean buildings
- Sixteen-dimensional locally compact translation planes with collineation groups of dimension at least 38
