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Forum Mathematicum

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Ed. by Brüdern, Jörg / Cohen, Frederick R. / Droste, Manfred / Duzaar, Frank / Neeb, Karl-Hermann / Noguchi, Junjiro / Shahidi, Freydoon / Sogge, Christopher D. / Wienhard, Anna

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Volume 20, Issue 1


A partial solution of the isoperimetric problem for the Heisenberg group

Donatella Danielli / Nicola Garofalo
  • Department of Mathematics, Purdue University, West Lafayette, IN 47907; Dip. Metodi e Modelli Matematici per le Scienze Applicate, Univ. Padova, 35100 Padova, Italy.
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/ Duy-Minh Nhieu
Published Online: 2008-03-11 | DOI: https://doi.org/10.1515/FORUM.2008.005


We provide a solution to the isoperimetric problem in the Heisenberg group ℍ 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.

2000 Mathematics Subject Classification: 53C17, 49K20.

About the article

Received: 2006-01-16

Revised: 2006-06-05

Published Online: 2008-03-11

Published in Print: 2008-01-01

Citation Information: Forum Mathematicum, Volume 20, Issue 1, Pages 99–143, ISSN (Online) 1435-5337, ISSN (Print) 0933-7741, DOI: https://doi.org/10.1515/FORUM.2008.005.

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