Gareth Speight

collaborators

5 papers

math.MG2026

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 $X \times_{I ¨} Y$ , where $X$ is a complete geodesic Gromov hyperbolic space, $Y$ is a compact geodesic metric space, and the warping fu…

math.MG2026

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 $C^{1}$ horizontal curve in a set of measure zero. This shows that the $C^{1}_{…

math.MG2025

Warped products, solid hyperbolic fillings, and the identity $D^{1, p} = N^{1, p} + R$

Ilmari Kangasniemi, Josh Kline, Nageswari Shanmugalingam +1

We construct a large class of metric measure spaces $Z$ which satisfy the identity $D^{1, p} (Z) = N^{1, p} (Z) + R$ , i.e.\ any measurable function $u : Z \to R$ …

math.DG2025

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…

math.FA2025

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…