3 papers
math.CA2026
Favard length and generalized projections
Izabella Laba, Alex McDonald, Krystal Taylor
We investigate generalized Favard lengths associated to smooth families of nonlinear projections. Under suitable regularity and transversality assumptions, we prove that generalize…
math.CA2025
Point configurations in sets of sufficient topological structure and a topological {E}rdÅs similarity conjecture
Alex McDonald, Krystal Taylor
We explore the occurrence of point configurations within non-meager (second category) Baire sets. A celebrated result of Steinhaus asserts that and contain an interval…
math.CA2025
Prescribed projections and efficient coverings by curves in the plane
Alan Chang, Alex McDonald, Krystal Taylor
Davies efficient covering theorem states that an arbitrary measurable set in the plane can be covered by full lines so that the measure of the union of the lines has the same m…