2022/04/06 by David, Guy C., Hook, Kevin
#28A75 #Classical Analysis and ODEs (math.CA) #FOS: Mathematics
paper · doi:10.48550/arxiv.2204.02933
We study the medial axis of a set K in Euclidean space (the set of points in space with more than one closest point in K) from a "coarse" and "quantitative" perspective. We show that on "most" balls B(x,r) in the complement of K, the set of almost-closest points to x in K takes up a small angle as seen from x. In other words, most locations and scales in the complement of K "appear" to fall outside the medial axis if one looks with only a certain finite resolution. The word "most" involves a Carleson packing condition, and our bounds are independent of the set K.