Esa Järvenpää, Maarit Järvenpää, Tamás Keleti
Published 2012-03-23Version 1
We study parametrized families of orthogonal projections for which the dimension of the parameter space is strictly less than that of the Grassmann manifold. We answer the natural question of how much the Hausdorff dimension may decrease by verifying the best possible lower bound for the dimension of almost all projections of a finite measure. We also show that a similar result is valid for smooth families of maps from $n$-dimensional Euclidean space to $m$-dimensional one.
Thickness and a gap lemma in $\mathbb{R}^d$
On the Hausdorff dimension of Furstenberg sets and orthogonal projections in the plane
On the distance sets spanned by sets of dimension $d/2$ in $\mathbb{R}^d$
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