Calculus of Variations and Geometric Measure Theory

R. Monti - F. Serra Cassano - D. Vittone

A negative answer to the Bernstein problem for intrinsic graphs in the Heisenberg group

created by vittone on 07 May 2008
modified on 03 May 2011


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


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