Sub-Riemannian calculus and monotonicity of the perimeter for graphical strips

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

doi:10.1007/s00209-009-0533-8

Sub-Riemannian calculus and monotonicity of the perimeter for graphical strips

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

Department of Mathematics

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

2 Scopus citations

Abstract

We consider the class of minimal surfaces given by the graphical strips S in the Heisenberg group H¹ and we prove that for points p along the center of H¹ the quantity is monotone increasing. Here, Q is the homogeneous dimension of H¹. We also prove that these minimal surfaces have maximum volume growth at infinity.

Original language	English
Pages (from-to)	617-637
Number of pages	21
Journal	Mathematische Zeitschrift
Volume	265
Issue number	3
DOIs	https://doi.org/10.1007/s00209-009-0533-8
State	Published - Jul 2010

Keywords

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

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10.1007/s00209-009-0533-8

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title = "Sub-Riemannian calculus and monotonicity of the perimeter for graphical strips",

abstract = "We consider the class of minimal surfaces given by the graphical strips S in the Heisenberg group H1 and we prove that for points p along the center of H1 the quantity is monotone increasing. Here, Q is the homogeneous dimension of H1. We also prove that these minimal surfaces have maximum volume growth at infinity.",

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.}",

note = "Funding Information: D. Danielli was supported in part by NSF grant CAREER DMS-0239771. N. Garofalo was supported in part by NSF Grant DMS-0701001.",

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AU - Danielli, D.

AU - Garofalo, N.

AU - Nhieu, D. M.

N1 - Funding Information: D. Danielli was supported in part by NSF grant CAREER DMS-0239771. N. Garofalo was supported in part by NSF Grant DMS-0701001.

PY - 2010/7

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N2 - We consider the class of minimal surfaces given by the graphical strips S in the Heisenberg group H1 and we prove that for points p along the center of H1 the quantity is monotone increasing. Here, Q is the homogeneous dimension of H1. We also prove that these minimal surfaces have maximum volume growth at infinity.

AB - We consider the class of minimal surfaces given by the graphical strips S in the Heisenberg group H1 and we prove that for points p along the center of H1 the quantity is monotone increasing. Here, Q is the homogeneous dimension of H1. We also prove that these minimal surfaces have maximum volume growth at infinity.

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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U2 - 10.1007/s00209-009-0533-8

DO - 10.1007/s00209-009-0533-8

M3 - 期刊論文

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SN - 0025-5874

VL - 265

SP - 617

EP - 637

JO - Mathematische Zeitschrift

JF - Mathematische Zeitschrift

IS - 3

ER -

Sub-Riemannian calculus and monotonicity of the perimeter for graphical strips

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Keywords

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