2 papers
math.MG2026
Illumination bodies for ball-convex bodies
Brandon Oliva, Elisabeth M. Werner, Diliya Yalikun
We introduce illumination bodies and weighted illumination bodies in the class of -dimensional -ball convex bodies. These bodies may be regarded as dual counterparts of the r…
math.CA2024
Quantitative metric density and connectivity for sets of positive measure
Guy C. David, Brandon Oliva
We show that in doubling, geodesic metric measure spaces (including, for example, Euclidean space), sets of positive measure have a certain large-scale metric density property. As…