Eotvos Lorand University, Budapest

Fri 19 Jan 2018, 2:00pm
Harmonic Analysis Seminar
MATH 126

Furstenbergtype estimates for unions of affine subspaces

MATH 126
Fri 19 Jan 2018, 2:00pm3:00pm
Abstract
A plane set is called a tFurstenberg set for some t in (0,1), if it has an at least tdimensional intersection with some line in each direction (here and in the sequel dimension refers to Hausdorff dimension). Classical results are that every tFurstenberg set has dimension at least 2t, and at least t + 1/2.
We generalize these estimates for families of affine subspaces. As a result, we prove that the union of any sdimensional family of kdimensional affine subspaces is at least k + s/(k+1) dimensional, and is exactly k + s dimensional if s is at most 1.
Based on joint work with Tamas Keleti and Andras Mathe.
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