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arXiv · 1801.06468

Projections of Gibbs measures on self-conformal sets

Catherine Bruce·Xiong Jin
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Abstract

We show that for Gibbs measures on self-conformal sets in $\mathbb{R}^d$ $(d\ge2)$ satisfying certain minimal assumptions, without requiring any separation condition, the Hausdorff dimension of orthogonal projections to $k$-dimensional subspaces is the same and is equal to the maximum possible value in all directions. As a corollary we show that Falconer's distance set conjecture holds for this class of self-conformal sets satisfying the open set condition.

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Catherine Bruce, Xiong Jin. 2018-05-15. Projections of Gibbs measures on self-conformal sets. https://doi.org/10.1088/1361-6544%2Faaec9f

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