4 papers
Prescribed projections for a general class of maps and efficient covering by variable plane curves
Alan Chang, Robert Fraser, Alex McDonald +2
We prove a prescribed projection theorem for any class of non-linear projections defined on open subsets of the plane which satisfies some mild geometric conditions. This generaliz…
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…
Point configurations in sets of sufficient topological structure and a topological {E}rdős 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…
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…