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

13 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

Access to Document

10.1090/S0002-9939-2011-11058-X

Cite this

@article{a4bee5d0b95a486993a5dd79b2c01ab2,

title = "Integrability of the sub-riemannian mean curvature of surfaces in the heisenberg group",

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.",

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

author = "D. Danielli and N. Garofalo and Nhieu, \{D. M.\}",

year = "2012",

doi = "10.1090/S0002-9939-2011-11058-X",

language = "English (US)",

volume = "140",

pages = "811--821",

journal = "Proceedings of the American Mathematical Society",

issn = "0002-9939",

publisher = "American Mathematical Society",

number = "3",

}

TY - JOUR

T1 - Integrability of the sub-riemannian mean curvature of surfaces in the heisenberg group

AU - Danielli, D.

AU - Garofalo, N.

AU - Nhieu, D. M.

PY - 2012

Y1 - 2012

N2 - 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.

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

UR - https://www.scopus.com/pages/publications/82255194069

UR - https://www.scopus.com/pages/publications/82255194069#tab=citedBy

U2 - 10.1090/S0002-9939-2011-11058-X

DO - 10.1090/S0002-9939-2011-11058-X

M3 - Article

SN - 0002-9939

VL - 140

SP - 811

EP - 821

JO - Proceedings of the American Mathematical Society

JF - Proceedings of the American Mathematical Society

IS - 3

ER -

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

Abstract

Keywords

ASJC Scopus subject areas

Access to Document

Other files and links

Fingerprint

Cite this