2008•Forum MathematicumOpen access

A partial solution of the isoperimetric problem for the Heisenberg group

Donatella Danielli, Nicola Garofalo, Duy-Minh Nhieu

Abstract

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.

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Key concepts: Isoperimetric inequality, Modulo, Mathematics, Heisenberg group, Isoperimetric dimension, Class (philosophy), Constant (computer programming), Combinatorics