On the Packing Dimension and Category of Exceptional Sets of Orthogonal Projections
arXiv:1204.2121 · doi:10.1007/s10231-014-0401-y
Abstract
We consider several classical results related to the Hausdorff dimension of exceptional sets of orthogonal projections and try to find out whether they have reasonable formulations in terms of packing dimension. We also investigate the existence of category versions for Marstrand and Falconer-Howroyd-type projection results.
42 pages, 5 figures. v3: improved Theorem 1.9
Cited by in corpus (13)
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- On the Assouad dimension of projections
- The Assouad dimensions of projections of planar sets
- Constancy results for special families of projections
- Assouad dimension influences the box and packing dimensions of orthogonal projections
- Projections of planar sets in well-separated directions
- Combinatorial proofs of two theorems of Lutz and Stull
- A discretised projection theorem in the plane
- Projections in vector spaces over finite fields
- A combinatorial proof of a sumset conjecture of Furstenberg
- Dimension and measure for generic continuous images
- Distance sets, orthogonal projections, and passing to weak tangents
- Exceptional projections of sets exhibiting almost dimension conservation