5 papers · 1 filter
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…
Arithmetic-progression gap sets in Cantor sets
Samantha Sandberg-Clark, Krystal Taylor, Alexia Yavicoli
We address the question of which common differences can arise in arithmetic progressions contained in fractal sets. For a compact set , we investigate not only w…
Applications of Nonlinear Projections to Rectifiable 1-sets
Rosemarie Bongers, Paige Bright, Caleb Marshall +1
Projection theorems in Euclidean space provide a fundamental link between the geometric structure of a set and the size of its lower-dimensional images. For 1-rectifiable sets in $…
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…
A Quantified Two-projection Theorem for Nonlinear Projections
Zhangze Li, Krystal Taylor
The classic Besicovitch projection theorem asserts that if a set is purely -unrectifiable with finite length in , its orthogonal projection has Lebesgue measure ze…