A partial solution of the isoperimetric problem for the Heisenberg group

We provide a partial solution to the isoperimetric problem in the Heisenberg group.Comment: 32 pages, 1 figur

First and second variation formulae for the sub-Riemannian area in three-dimensional pseudo-hermitian manifolds

We calculate the first and the second variation formula for the sub-Riemannian area in three dimensional pseudo-hermitian manifolds. We consider general variations that can move the singular set of a C^2 surface and non-singular variation for C_H^2 surfaces. These formulas enable us to construct a stability operator for non-singular C^2 surfaces and another one for C2 (eventually singular) surfaces. Then we can obtain a necessary condition for the stability of a non-singular surface in a pseudo-hermitian 3-manifold in term of the pseudo-hermitian torsion and the Webster scalar curvature. Finally we classify complete stable surfaces in the roto-traslation group RT .Comment: 36 pages. Misprints corrected. Statement of Proposition 9.8 slightly changed and Remark 9.9 adde

The Bernstein Problem for Embedded Surfaces in the Heisenberg Group H

In the paper [13] we proved that the only stable C 2 minimal surfaces in the first Heisenberg group H 1 which are graphs over some plane and have empty characteristic locus must be vertical planes. This result represents a sub-Riemannian version of the celebrated theorem of Bernstein. In this paper we extend the result in [13] to C 2 complete em-bedded minimal surfaces in H 1 with empty characteristic locus. We prove that every such a surface without boundary must be a vertical plane. This result represents a sub-Riemannian coun-terpart of the classical theorems of Fischer-Colbrie and Schoen, [16], and do Carmo and Peng, [15], and answers a question posed by Lei Ni

A convenient and robust in vivo reporter system to monitor gene expression in the human pathogen helicobacter pylori

Thirty years of intensive research have significantly contributed to our understanding of Helicobacter pylori biology and pathogenesis. However, the lack of convenient genetic tools, in particular the limited effectiveness of available reporter systems, has notably limited the toolbox for fundamental and applied studies. Here, we report the construction of a bioluminescent H. pylori reporter system based on the Photorhabdus luminescens luxCDABE cassette. The system is constituted of a promoterless lux acceptor strain in which promoters and sequences of interest can be conveniently introduced by double homologous recombination of a suicide transformation vector. We validate the robustness of this new lux reporter system in noninvasive in vivo monitoring of dynamic transcriptional responses of inducible as well as repressible promoters and demonstrate its suitability for the implementation of genetic screens in H. pylori. © 2012, American Society for Microbiology

Sub-Riemannian Calculus on Hypersurfaces in Carnot Groups

We develope basic geometric quantities and properties of hypersurfaces in Carnot groups

Basic properties of nonsmooth Hormander's vector fields and Poincare's inequality

We consider a family of vector fields defined in some bounded domain of R^p, and we assume that they satisfy Hormander's rank condition of some step r, and that their coefficients have r-1 continuous derivatives. We extend to this nonsmooth context some results which are well-known for smooth Hormander's vector fields, namely: some basic properties of the distance induced by the vector fields, the doubling condition, Chow's connectivity theorem, and, under the stronger assumption that the coefficients belong to C^{r-1,1}, Poincare's inequality. By known results, these facts also imply a Sobolev embedding. All these tools allow to draw some consequences about second order differential operators modeled on these nonsmooth Hormander's vector fields.Comment: 60 pages, LaTeX; Section 6 added and Section 7 (6 in the previous version) changed. Some references adde

Analysis of static and dynamic balance in healthy elderly practitioners of Tai Chi Chuan versus ballroom dancing

OBJECTIVE: To determine whether Tai Chi Chuan or ballroom dancing promotes better performance with respect to postural balance, gait, and postural transfer among elderly people. METHODS: We evaluated 76 elderly individuals who were divided into two groups: the Tai Chi Chuan Group and the Dance Group. The subjects were tested using the NeuroCom Balance Master¯ force platform system with the following protocols: static balance tests (the Modified Clinical Tests of Sensory Interaction on Balance and Unilateral Stance) and dynamic balance tests (the Walk Across Test and Sit-to-stand Transfer Test). RESULTS: In the Modified Clinical Test of Sensory Interaction on Balance, the Tai Chi Chuan Group presented a lower sway velocity on a firm surface with open and closed eyes, as well as on a foam surface with closed eyes. In the Modified Clinical Test of Sensory Interaction on Unilateral Stance, the Tai Chi Chuan Group presented a lower sway velocity with open eyes, whereas the Dance Group presented a lower sway velocity with closed eyes. In the Walk Across Test, the Tai Chi Chuan Group presented faster walking speeds than those of the Dance Group. In the Sit-to-stand Transfer Test, the Tai Chi Chuan Group presented shorter transfer times from the sitting to the standing position, with less sway in the final standing position. CONCLUSION: The elderly individuals who practiced Tai Chi Chuan had better bilateral balance with eyes open on both types of surfaces compared with the Dance Group. The Dance Group had better unilateral postural balance with eyes closed. The Tai Chi Chuan Group had faster walking speeds, shorter transfer times, and better postural balance in the final standing position during the Sit-to-stand Test