Inserted: 7 may 2008
Last Updated: 3 may 2011
Journal: Boll. Unione Mat. Ital. (9)
A negative answer to the Bernstein problem for entire $\mathbb H$-perimeter minimizing intrinsic graphs is given in the setting of the first Heisenberg group $\mathbb H^1$ endowed with its Carnot-Carath´eodory metric structure. Moreover, in all Heisenberg groups $\mathbb H^n$ an area formula for intrinsic graphs with Sobolev regularity is provided, together with the associated first and second variation formulae.
Keywords: Heisenberg group, Intrinsic graphs, Bernstein problem