Interior, Dimension, and Measure of Algebraic Sums of Planar Sets and Curves

Fractal Geometry and Dynamics

23 November 14:00 - 14:50

Krystal Taylor - Ohio State University

Recently considerable attention has been given to the study of the arithmetic sums of two planar sets A + Г := {a + g : a ∈ A, g ∈ Г} . We focus on the case when Г is a piecewise C2 curve, in particular when Г is the unit circle. There is a natural guess what the size (Hausdorff dimension, Lebesgue measure) of A + Г should be. We verify this under some simple natural assumptions. We also address the more difficult question: under which condition does the set A + Г have non-empty interior? Particular emphasis is given to the case when the Hausdorff dimension of the set A is 1. This is joint work with Karoly Simon.

Kenneth J. Falconer
University of St Andrews
Maarit Järvenpää
University of Oulu
Antti Kupiainen
University of Helsinki
Francois Ledrappier
University of Notre Dame
Pertti Mattila
University of Helsinki


Maarit Järvenpää


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