@article{529b75e9db8243f4a8166e1a49fc9ecd,
title = "Sub-Riemannian calculus on hypersurfaces in Carnot groups",
abstract = "We develop a sub-Riemannian calculus for hypersurfaces in graded nilpotent Lie groups. We introduce an appropriate geometric framework, such as horizontal Levi-Civita connection, second fundamental form, and horizontal Laplace-Beltrami operator. We analyze the relevant minimal surfaces and prove some basic integration by parts formulas. Using the latter we establish general first and second variation formulas for the horizontal perimeter in the Heisenberg group. Such formulas play a fundamental role in the sub-Riemannian Bernstein problem.",
keywords = "First and second variation of the horizontal perimeter, H-mean curvature, Horizontal Levi-Civita connection, Horizontal second fundamental form, Intrinsic integration by parts",
author = "D. Danielli and N. Garofalo and Nhieu, {D. M.}",
note = "Funding Information: * Corresponding author. E-mail addresses: danielli@math.purdue.edu (D. Danielli), garofalo@math.purdue.edu (N. Garofalo), nhieu@math.georgetown.edu (D.M. Nhieu). 1 Supported in part by NSF grants DMS-0002801 and CAREER DMS-0239771. 2 Supported in part by NSF Grant DMS-0300477.",
year = "2007",
month = oct,
day = "20",
doi = "10.1016/j.aim.2007.04.004",
language = "???core.languages.en_GB???",
volume = "215",
pages = "292--378",
journal = "Advances in Mathematics",
issn = "0001-8708",
number = "1",
}