Research

My research interests lie in Carnot-Caratheodory geometry.  Recently, I have been focusing on minimal and isoperimetric surface problems in Carnot groups and applications. 

 

Here is a list of papers and preprints.  Most can be found on arxiv.org, but the versions below (if available) are likely up to date and (perhaps) have better quality pictures.

 

1. “The large scale geometry of nilpotent Lie groups”, Comm. Anal. Geom., 9 (2001), no. 5, 951-982.

2. “A notion of rectifiability modeled on Carnot groups”, Indiana Univ. Math. J. 53 (2004), 49-82.

3. “Minimal surfaces in the Heisenberg group”, Geom. Ded. 104 (2004), 201-231.

4. “The Bernstein problem in the Heisenberg group”, joint with N. Garofalo, submitted.

5. “C¹ hypersurfaces of the Heisenberg group are N-rectifiable”, joint with D. Cole, submitted.

6. “H-minimal graphs of low regularity”, to appear, Comm. Math. Helv.

7. “Constant mean curvature surfaces in sub-Riemannain spaces”, joint with R. Hladky, submitted.

8. “An invitation to the isoperimetric problem”, joint with L. Capogna and J. Tyson, in preparation.

9. “Minimal surfaces in the Roto-translation group with applications to a neuro-biological image completion model”, joint with R. Hladky, submitted.

10. “A disocclusion algorithm based on a model of the visual cortex”, joint with R. Hladky, in preparation.