Hausdorff dimension estimates for restricted families of projections in R3R3

This paper is concerned with restricted families of projections in R3R3. Let K⊂R3K⊂R3 be a Borel set with Hausdorff dimension dim⁡K=s>1dim⁡K=s>1. If GG is a smooth and sufficiently well-curved one-dimensional family of two-dimensional subspaces, the main result states that there exists σ(s)>1σ(s)>1 such that dim⁡πV(K)≥σ(s)dim⁡πV(K)≥σ(s) for almost all V∈GV∈G. A similar result is obtained for some specific families of one-dimensional subspaces.