56 citations · 90 across the 4 of their papers we have counts for
6 papers · 1 filter
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,…
The large scale geometry of nilpotent Lie groups
Scott Pauls
In this paper, we prove results concerning the large scale geometry of connected, simply connected nonabelian nilpotent Lie groups equipped with left invariant Riemannian metrics.…