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- Scott D. Pauls
- 2006

In this paper we investigate H-minimal graphs of lower regularity. We show that noncharactersitic C H-minimal graphs whose components of the unit horizontal Gauss map are in W 1,1 are ruled surfacesâ€¦ (More)

- Gregory Leibon, Scott D. Pauls, Daniel N. Rockmore, ROBERT SAVELL A BSTRACT
- 2008

We present a new method for articulating scale-dependent topological descriptions of the network structure inherent in many complex systems. The technique is based on â€œPartition Decoupled Nullâ€¦ (More)

- Scott D. Pauls
- 1998

In this paper, we prove results concerning the large scale geometry of connected, simply connected nilpotent Lie groups equipped with left invariant Riemannian metrics. Precisely, we prove that thereâ€¦ (More)

- Robert K. Hladky, Scott D. Pauls
- Journal of Mathematical Imaging and Vision
- 2009

We investigate solutions to the minimal surface problem with Dirichlet boundary conditions in the roto-translation group equipped with a sub-Riemannian metric. By work of G. Citti and A. Sarti, suchâ€¦ (More)

- Scott D. Pauls
- 2004

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 Nrectifiable if it is the Lipschitzâ€¦ (More)

- Luca Capogna, Scott D. Pauls, JEREMY T. TYSON
- 2010

We use a Riemannian approximation scheme to give a characterization for smooth convex functions on a Carnot group (in the sense of Danielliâ€“Garofaloâ€“ Nhieu or Luâ€“Manfrediâ€“Stroffolini) in terms of theâ€¦ (More)

We derive a formula for the first variation of horizontal perimeter measure for C2 hypersurfaces of completely general sub-Riemannian manifolds, allowing for the existence of characteristic points.â€¦ (More)

- Scott D. Pauls, Daniel Remondini
- Physical review. E, Statistical, nonlinear, andâ€¦
- 2012

We introduce a family of new centralities, the k-spectral centralities. k-spectral centrality is a measurement of importance with respect to the deformation of the graph Laplacian associated with theâ€¦ (More)

- Daryl R. DeFord, Scott D. Pauls
- ArXiv
- 2017

Multiplex networks offer an important tool for the study of complex systems and extending techniques originally designed for singleâ€“layer networks is an important area of study. One of the mostâ€¦ (More)

- Daniele Danielli, NicolÃ¡s GarÃ³falo, D. M. Nhieu, Scott D. Pauls
- 2010

In the first Heisenberg group H with its sub-Riemannian structure generated by the horizontal subbundle, we single out a class of C non-characteristic entire intrinsic graphs which we call strictâ€¦ (More)