Hausdorff dimension, projections, intersections, and Besicovitch sets
Pertti Mattila
TL;DR
This survey reviews recent advances in understanding the Hausdorff dimension of projections, intersections, and Besicovitch sets in Euclidean spaces, focusing on exceptional set estimates and restricted projections.
Contribution
It synthesizes recent results on Hausdorff dimension estimates for projections and intersections, highlighting connections with Besicovitch sets and exceptional set analysis.
Findings
Recent bounds on Hausdorff dimension of projections and intersections
Estimates of exceptional sets in projection theorems
Relations between projections and Besicovitch sets
Abstract
This is a survey on recent developments on the Hausdorff dimension of projections and intersections for general subsets of Euclidean spaces, with an emphasis on estimates of the Hausdorff dimension of exceptional sets and on restricted projection families. We shall also discuss relations between projections and Hausdorff dimension of Besicovitch sets.
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Taxonomy
TopicsAdvanced Topology and Set Theory · Advanced Banach Space Theory · Approximation Theory and Sequence Spaces