10 citations · 37 across the 19 of their papers we have counts for
13 papers · 1 filter
Quantitative differentiation and the medial axis
Guy C. David, Kevin Hook
We study the medial axis of a set in Euclidean space (the set of points in space with more than one closest point in ) from a "coarse" and "quantitative" perspective. We sho…
Quantitative straightening of distance spheres
Guy C. David, McKenna Kaczanowski, Dallas Pinkerton
We study "distance spheres": the set of points lying at constant distance from a fixed arbitrary subset of . We show that, away from the regions where is "too dens…
A local description of 2-dimensional almost minimal sets bounded by a curve
Guy David
We study the local regularity of sliding almost minimal sets of dimension 2 in , bounded by a smooth curve . These are a good way to model soap films bounded by a curve, a…
Sliding almost minimal sets and the Plateau problem
Guy David
We present some old and recent regularity results concerning minimal and almost minimal sets in domains of the Euclidean space. We concentrate on a sliding variant of Almgren's not…
Wasserstein Distance and the Rectifiability of Doubling Measures: Part I
Jonas Azzam, Guy David, Tatiana Toro
Let be a doubling measure in . We investigate quantitative relations between the rectifiability of and its distance to flat measures. More precisely, for …
Local regularity properties of almost- and quasiminimal sets with a sliding boundary condition
Guy David
We study the boundary regularity of almost minimal and quasiminimal sets that satisfy sliding boundary conditions. The competitors of a set are defined as , where $…