56 citations · 90 across the 4 of their papers we have counts for
7 papers
Constant mean curvature surfaces in sub-Riemannian geometry
Robert K. Hladky, Scott D. Pauls
We investigate the minimal and isoperimetric surface problems in a large class of sub-Riemannian manifolds, the so-called Vertically Rigid spaces. We construct an adapted connectio…
H-minimal graphs of low regularity in the Heisenberg group
Scott D. Pauls
In this paper we investigate H-minimal graphs of lower regularity. We show that noncharactersitic C^1 H-minimal graphs whose components of the unit horizontal Gauss map are in W^{1…
C^1 Hypersurfaces of the Heisenberg Group are N-Rectifiable
Daniel R. Cole, Scott D. Pauls
We show that C^1 hypersurfaces in the Heisenberg group are countably N-rectifiable. As a corollary, this shows that all C^1_H graphs over the xy-plane are countable N-rectifiable,…
The Bernstein Problem in the Heisenberg Group
Nicola Garofalo, Scott D. Pauls
We establish the following theorem of Bernstein type for the first Heisenberg group: Let S be a C^2 connected H-minimal surface which is a graph over some plane P, then S is either…
Minimal surfaces in the Heisenberg group
Scott D. Pauls
We investigate the minimal surface problem in the three dimensional Heisenberg group, H, equipped with its standard Carnot-Caratheodory metric. Using a particular surface measure,…
A notion of rectifiability modeled on Carnot groups
Scott D. Pauls
We introduce a notion of rectifiability modeled on Carnot groups. Precisely, we say that a subset E of a Carnot group M and N is a subgroup of M, we say E is N-rectifiable if it is…