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- W2786453073 abstract "We study dimensions of sumsets and iterated sumsets and provide natural conditions which guarantee that a set $F subseteq mathbb{R}$ satisfies $overline{dim}_text{B} F+F > overline{dim}_text{B} F$ or even $dim_text{H} n F to 1$. Our results apply to, for example, all uniformly perfect sets, which include Ahlfors-David regular sets. Our proofs rely on Hochman's inverse theorem for entropy and the Assouad and lower dimensions play a critical role. We give several applications of our results including an ErdH{o}s-Volkmann type theorem for semigroups and new lower bounds for the box dimensions of distance sets for sets with small dimension." @default.
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- W2786453073 date "2018-02-09" @default.
- W2786453073 modified "2023-09-27" @default.
- W2786453073 title "Dimension growth for iterated sumsets" @default.
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