9 citations · 30 across the 11 of their papers we have counts for
14 papers
On planar Nikodym-type sets
Alan Chang, Mingfeng Chen, Shaoming Guo +3
Nikodym constructed a measure-zero Borel set in the plane that contains a punctured line segment passing through each point in the unit square. Fenton and Falconer asked whether a…
Favard length of non-homogeneous random disc-like Cantor sets
Alan Chang, Damian Dąbrowski, Giacomo Del Nin
The Favard length of a planar set is the average length of its orthogonal projections. We provide sharp estimates for the Favard length decay of a random variant of the non-homogen…
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…
Sharp Favard length of random Cantor sets
Alan Chang, Pablo Shmerkin, Ville Suomala
We show that for a large class of planar -dimensional random fractals , the Favard length of the neighborhood is comparable to $\log^{-1}(1/…
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…
A random line intersects in two probabilistically independent locations
Dmitriy Bilyk, Alan Chang, Otte Heinävaara +2
We consider random lines in (random with respect to the kinematic measure) and how they intersect . It is known that the entry point and the exit point…
Nikodym sets and maximal functions associated with spheres
Alan Chang, Georgios Dosidis, Jongchon Kim
We study spherical analogues of Nikodym sets and related maximal functions. In particular, we prove sharp -estimates for Nikodym maximal functions associated with spheres. As…
Structure of sets with nearly maximal Favard length
Alan Chang, Damian Dąbrowski, Tuomas Orponen +1
Let be an measurable set with , and let be a line segment with $\mat…
Decoupling for fractal subsets of the parabola
Alan Chang, Jaume de Dios Pont, Rachel Greenfeld +3
We consider decoupling for a fractal subset of the parabola. We reduce studying decoupling for a fractal subset on the parabola to stu…
Analytic capacity and projections
Alan Chang, Xavier Tolsa
In this paper we study the connection between the analytic capacity of a set and the size of its orthogonal projections. More precisely, we prove that if is co…
Small unions of affine subspaces and skeletons via Baire category
Alan Chang, Marianna Csörnyei, Kornélia Héra +1
Our aim is to find the minimal Hausdorff dimension of the union of scaled and/or rotated copies of the -skeleton of a fixed polytope centered at the points of a given set. For m…
The Kakeya needle problem and the existence of Besicovitch and Nikodym sets for rectifiable sets
Alan Chang, Marianna Csörnyei
We solve the Kakeya needle problem and construct a Besicovitch and a Nikodym set for rectifiable sets.
The Whitney extension theorem in high dimensions
Alan Chang
We prove a variant of the standard Whitney extension theorem for , in which the norm of the extension operator has polynomial growth in for fixed …
Newman's conjecture in various settings
Julio Andrade, Alan Chang, Steven J. Miller
De Bruijn and Newman introduced a deformation of the Riemann zeta function , and found a real constant which encodes the movement of the zeros of under the deforma…