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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.

A partial solution of the isoperimetric problem for the Heisenberg group