Tuomas Sahlsten

Absolute continuity of projections and dimension conservation for self-similar sets and measures

Let $A\subset\mathbb{R}^d$, $d\geq3$, be the attractor of a self-similar IFS whose rotations generate a dense subgroup of $\mathrm{SO}(d)$. For every $1\leq k<\dim_{\mathrm{H}} A$ and $V\in\mathrm{Gr}(d,k)$, we prove that $\pi_VA$ has positive $k$-dimensional Lebesgue measure uniformly in $V$, and $\dim_{\mathrm{H}}(A\...