Integrability of the sub-riemannian mean curvature of surfaces in the heisenberg group

D. Danielli; N. Garofalo; D. M. Nhieu

doi:10.1090/S0002-9939-2011-11058-X

Integrability of the sub-riemannian mean curvature of surfaces in the heisenberg group

D. Danielli, N. Garofalo, D. M. Nhieu

Research output: Contribution to journal › Article › peer-review

11 Scopus citations

Abstract

The problem of the local summability of the sub-Riemannian mean curvature H of a hypersurface M in the Heisenberg group, or in more general Carnot groups, near the characteristic set of M arises naturally in several questions in geometric measure theory. We construct an example which shows that the sub-Riemannian mean curvature H of a C² surface M in the Heisenberg group H¹ in general fails to be integrable with respect to the Riemannian volume on M.

Original language	English (US)
Pages (from-to)	811-821
Number of pages	11
Journal	Proceedings of the American Mathematical Society
Volume	140
Issue number	3
DOIs	https://doi.org/10.1090/S0002-9939-2011-11058-X
State	Published - 2012
Externally published	Yes

Keywords

First and second variation
H-mean curvature
Integration by parts
Minimal surfaces
Monotonicity of the H-perimeter

ASJC Scopus subject areas

General Mathematics
Applied Mathematics

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10.1090/S0002-9939-2011-11058-X

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AU - Garofalo, N.

AU - Nhieu, D. M.

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AB - The problem of the local summability of the sub-Riemannian mean curvature H of a hypersurface M in the Heisenberg group, or in more general Carnot groups, near the characteristic set of M arises naturally in several questions in geometric measure theory. We construct an example which shows that the sub-Riemannian mean curvature H of a C2 surface M in the Heisenberg group H1 in general fails to be integrable with respect to the Riemannian volume on M.

KW - First and second variation

KW - H-mean curvature

KW - Integration by parts

KW - Minimal surfaces

KW - Monotonicity of the H-perimeter

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Integrability of the sub-riemannian mean curvature of surfaces in the heisenberg group

Abstract

Keywords

ASJC Scopus subject areas

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