Positive harmonic functions on the Heisenberg group II

Minimal Surfaces and Harmonic Functions in the Heisenberg Group

We study the blow-up of H-perimeter minimizing sets in the Heisenberg group H, n ≥ 2. We show that the Lipschitz approximations rescaled by the square root of excess converge to a limit function. Assuming a stronger notion of local minimality, we prove that this limit function is harmonic for the Kohn Laplacian in a lower dimensional Heisenberg group.

Convex Functions on the Heisenberg Group

Convex functions in Euclidean space can be characterized as universal viscosity subsolutions of all homogeneous fully nonlinear second order elliptic partial differential equations. This is the starting point we have chosen for a theory of convex functions on the Heisenberg group.

ON THE REGULARITY OF p-HARMONIC FUNCTIONS IN THE HEISENBERG GROUP by

On the axiomatic of harmonic functions II

© Annales de l’institut Fourier, 1963, tous droits réservés. L’accès aux archives de la revue « Annales de l’institut Fourier » (http://annalif.ujf-grenoble.fr/) implique l’accord avec les conditions générales d’utilisation (http://www.numdam.org/legal.php). Toute utilisation commerciale ou impression systématique est constitutive d’une infraction pénale. Toute copie ou impression de ce fichier...

The Heisenberg group and Hermite functions