TheauthorsdefinetheGaussmapofsurfacesinthethree-dimensionalHeisenberggroupandgivearepresentationformulaforsurfacesofprescribedmeancurvature.Furthermore,asecondorderpartialdifferentialequationfortheGaussmapisobtained,anditisshownthatthisequationisthecompleteintegrabilityconditionoftherepresentation.