Published Paper

Inserted: 7 may 2008
Last Updated: 3 may 2011

Journal: Boll. Unione Mat. Ital. (9)
Volume: 1
Number: 3
Pages: 709-727
Year: 2008

Abstract:

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

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