# Constant mean curvature surfaces in sub-Riemannian geometry

## Scott Pauls (Department of Mathematics, Dartmouth College)

created by magnani on 12 Jan 2006

25 jan 2006

Abstract.

On Wednesday 25 January, at 14:30 in Sala delle Riunioni'' of the Mathematics Department

Scott Pauls, from Dartmouth College (U.S.)

will speak of "Constant mean curvature surfaces in sub-Riemannian geometry"

The abstract follows:

In 1996, Garofalo and Nhieu showed the existence of solutions to the Plateau Problem in the setting of sub-Riemannian spaces, beginning close to a decade of sustained investigation of minimal surfaces in sub-Riemannian spaces. In this talk, we will focus on a first example, the sub-Riemannian Heisenberg group, to describe the current state of knowledge. While smooth minimal surfaces have some remarkable rigidity properties, we will discuss new constructions of minimal surfaces of lower regularity, some of which can be shown to be minimizers. If time permits, we will discuss extensions of these ideas to the minimal surface problem in the roto-translation group which has direct application to a model of the function of the first layer of the visual cortex (due to G. Citti and A. Sarti) and to recent digital inpainting algorithms (due to L. Ambrosio and S. Masnou).

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