4 citations · 4 across the 5 of their papers we have counts for
5 papers
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 $…
Energy-minimizing measures supported near fractal 1-sets
Rosemarie Bongers
Energy techniques can be used to study the structure of fractal sets; the existence of a measure with finite Riesz energy supported on a set gives information about its dimension,…
Minimal Constructible Sets
Jorge Garcia, Rosemarie Bongers, Jonathan Detgen +1
Given an initial family of sets, we may take unions, intersections and complements of the sets contained in this family in order to form a new collection of sets; our construction…
Transversal families of nonlinear projections and generalizations of Favard length
Rosemarie Bongers, Krystal Taylor
Projections detect information about the size, geometric arrangement, and dimension of sets. To approach this, one can study the energies of measures supported on a set and the ene…
Geometric Bounds for Favard Length
Rosemarie Bongers
Given a set in the plane, the average length of its projections over all directions is called Favard length. This quantity measures the size of a set, and is closely related to met…