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math.CA2024
Self-similar sets and Lipschitz graphs
Blair Davey, Silvia Ghinassi, Bobby Wilson
We investigate and quantify the distinction between rectifiable and purely unrectifiable 1-sets in the plane. That is, given that purely unrectifiable 1-sets always have null inter…
math.CA2021
A Quantification of a Besicovitch Nonlinear Projection Theorem via Multiscale Analysis
Blair Davey, Krystal Taylor
The Besicovitch projection theorem states that if a subset of the plane has finite length in the sense of Hausdorff measure and is purely unrectifiable (so its intersection wit…
math.CA2020
Upper and lower bounds on the rate of decay of the Favard curve length for the four-corner Cantor set
Laura Cladek, Blair Davey, Krystal Taylor
The Favard length of a subset of the plane is defined as the average of its orthogonal projections. This quantity is related to the probabilistic Buffon needle problem; that is, th…