Dimensions of sums with self-similar sets
Daniel Oberlin, Richard Oberlin
TL;DR
This paper investigates how the Minkowski dimension of the sum of a self-similar set and another set relates to the dimensions of each, providing lower bounds under certain conditions.
Contribution
It establishes new lower bounds for the Minkowski dimension of sums involving self-similar sets and arbitrary sets in Euclidean space.
Findings
Derived lower bounds for Minkowski dimensions of sums with self-similar sets.
Extended understanding of the additive properties of fractal dimensions.
Provided conditions under which these bounds hold.
Abstract
For some self-similar sets K in d-dimensional Euclidean space we obtain certain lower bounds for the lower Minkowski dimension of K+E in terms of the lower Minkowski dimension of E.
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