A negative answer to the Bernstein problem for entire H-perimeter minimizing intrinsic graphs is given in the setting of the first Heisenberg group H^1 endowed with its Carnot-Carathéodory metric structure. Moreover, in all Heisenberg groups H^n an area formula for intrinsic graphs with Sobolev regularity is provided, together with the associated first and second variation formulae.
A negative answer to the Bernstein problem for intrinsic graphs in the Heisenberg group
MONTI, ROBERTO;VITTONE, DAVIDE
2008
Abstract
A negative answer to the Bernstein problem for entire H-perimeter minimizing intrinsic graphs is given in the setting of the first Heisenberg group H^1 endowed with its Carnot-Carathéodory metric structure. Moreover, in all Heisenberg groups H^n an area formula for intrinsic graphs with Sobolev regularity is provided, together with the associated first and second variation formulae.
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