29 citations · 43 across the 21 of their papers we have counts for
29 papers
Warped product spaces: Gromov hyperbolicity and identification of the visual boundary
Josh Kline, Nageswari Shanmugalingam, Gareth Speight +1
In this paper, we consider warped product spaces , where is a complete geodesic Gromov hyperbolic space, is a compact geodesic metric space, and the warping fun…
A Lipschitz curve in a Carnot group that is purely unrectifiable by smooth horizontal curves
Gareth Speight, Scott Zimmerman
We construct a Lipschitz curve in the free Carnot group of step 3 with 2 generators that meets every horizontal curve in a set of measure zero. This shows that the $C^{1}_{…
Warped products, solid hyperbolic fillings, and the identity
Ilmari Kangasniemi, Josh Kline, Nageswari Shanmugalingam +1
We construct a large class of metric measure spaces which satisfy the identity , i.e.\ any measurable function …
Directional Pliability, Whitney Extension, and Lusin Approximation for Curves in Carnot Groups
Gareth Speight, Scott Zimmerman
We show that, in arbitrary Carnot groups, pliability in a subset of directions is sufficient to guarantee the existence of a Whitney-type extension and a Lusin approximation for cu…
Universal Differentiability Sets in Laakso Space
Sylvester Eriksson-Bique, Andrea Pinamonti, Gareth Speight
We show that there exists a family of mutually singular doubling measures on Laakso space with respect to which real-valued Lipschitz functions are almost everywhere differentiable…
Higher order Whitney extension and Lusin approximation for Horizontal curves in the Heisenberg group
Andrea Pinamonti, Gareth Speight, Scott Zimmerman
In the setting of horizontal curves in the Heisenberg group, we prove a finiteness principle, a Lusin approximation result, a Whitney extension res…