9 papers
Arithmetic-progression gap sets in Cantor sets
Samantha Sandberg, Samantha Sandberg-Clark, Krystal Taylor +1
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…
Triangles in the Plane and arithmetic progressions in thick compact subsets of
Samantha Sandberg-Clark, Krystal Taylor
This article focuses on the occurrence of 3-point configurations in subsets of of sufficient thickness. We prove that a compact set contains…
Interior of distance trees over thin Cantor sets
Yeonwook Jung, Krystal Taylor
It is known that if a compact set in has Hausdorff dimension greater than , then its -chain distance set $$Î^n(E) = \left\{\left(\left|x^1-x^2\right…