6 citations · 10 across the 6 of their papers we have counts for
7 papers
Minimizers of the Maximum Distance Problem via an Analyst's Traveling Salesperson Algorithm
Enrique Alvarado, Silvia Ghinassi, Lisa Naples
We provide an upper and lower bound for the length of Maximum Distance Problem minimizers in terms of a finite scale geometric square sum.
Asymptotics of maximum distance minimizers
Enrique G Alvarado, Louisa Catalano, Tomás Merchán +1
We study the limiting behavior of -maximum distance minimizers and the asymptotics of their -dimensional Hausdorff measures as tends to zero in several contexts, includin…
Non-existence of cusps for degenerate Alt-Caffarelli functionals
Sean McCurdy, Lisa Naples
We eliminate the existence of cusps in a class of \textit{degenerate} free-boundary problems for the Alt-Caffarelli functional $J_{Q}(v, Ω):= \int_Ω|\nabla v|^2 + Q^2(x)χ_{\{v>0\}}…
Nilpotent groups and biLipschitz embeddings into
Sylvester Eriksson-Bique, Chris Gartland, Enrico Le Donne +2
We prove that if a simply connected nilpotent Lie group quasi-isometrically embeds into an space, then it is abelian. We reach this conclusion by proving that every Carnot gr…
Radon measures and Lipschitz graphs
Matthew Badger, Lisa Naples
For all , we investigate the interaction of locally finite measures in with the family of -dimensional Lipschitz graphs. For instance, we charact…
Rectifiability of pointwise doubling measures in Hilbert Space
Lisa Naples
In geometric measure theory, there is interest in studying the interaction of measures with rectifiable sets. Here, we extend a theorem of Badger and Schul in Euclidean space to ch…
Hölder curves and parameterizations in the Analyst's Traveling Salesman theorem
Matthew Badger, Lisa Naples, Vyron Vellis
We investigate the geometry of sets in Euclidean and infinite-dimensional Hilbert spaces. We establish sufficient conditions that ensure a set of points is contained in the image o…