A partial solution of the isoperimetric problem for the Heisenberg group

Donatella Danielli; Nicola Garofalo; Duy Minh Nhieu; Giorgio Talenti

doi:10.1515/FORUM.2008.005

A partial solution of the isoperimetric problem for the Heisenberg group

Donatella Danielli, Nicola Garofalo, Duy Minh Nhieu, Giorgio Talenti

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

22 Scopus citations

Abstract

We provide a solution to the isoperimetric problem in the Heisenberg group ⁿ when the competing sets belong to a restricted class of C ² graphs. Within this restricted class we characterize the isoperimetric profiles as the bubble sets (1.5) (modulo nonisotropic dilations and left-translations). We also compute the isoperimetric constant.

Original language	English (US)
Pages (from-to)	99-143
Number of pages	45
Journal	Forum Mathematicum
Volume	20
Issue number	1
DOIs	https://doi.org/10.1515/FORUM.2008.005
State	Published - Jan 1 2008
Externally published	Yes

ASJC Scopus subject areas

General Mathematics
Applied Mathematics

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10.1515/FORUM.2008.005

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author = "Donatella Danielli and Nicola Garofalo and Nhieu, {Duy Minh} and Giorgio Talenti",

note = "Funding Information: First author supported in part by NSF grants DMS-0002801 and CAREER DMS-0239771. Second author supported in part by NSF Grants DMS-0070492 and DMS-0300477.",

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AU - Nhieu, Duy Minh

AU - Talenti, Giorgio

N1 - Funding Information: First author supported in part by NSF grants DMS-0002801 and CAREER DMS-0239771. Second author supported in part by NSF Grants DMS-0070492 and DMS-0300477.

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N2 - We provide a solution to the isoperimetric problem in the Heisenberg group n when the competing sets belong to a restricted class of C 2 graphs. Within this restricted class we characterize the isoperimetric profiles as the bubble sets (1.5) (modulo nonisotropic dilations and left-translations). We also compute the isoperimetric constant.

AB - We provide a solution to the isoperimetric problem in the Heisenberg group n when the competing sets belong to a restricted class of C 2 graphs. Within this restricted class we characterize the isoperimetric profiles as the bubble sets (1.5) (modulo nonisotropic dilations and left-translations). We also compute the isoperimetric constant.

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A partial solution of the isoperimetric problem for the Heisenberg group

Abstract

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