The orbit method of Kirillov is used to derive the p-mechanical brackets [25]. They generate the quantum (Moyal) and classic (Poisson) brackets on respective orbits corresponding to representations of the Heisenberg group. The extension of p-mechanics to field theory is made through the De Donder–Weyl Hamiltonian formulation. The principal step is the substitution of the Heisenberg group with G...

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.

The orbit method of Kirillov is used to derive the p-mechanical brackets [25]. They generate the quantum (Moyal) and classic (Poisson) brackets on respective orbits corresponding to representations of the Heisenberg group. The extension of p-mechanics to field theory is made through the De Donder–Weyl Hamiltonian formulation. The principal step is the substitution of the Heisenberg group with G...

Heisenberg groups are simply connected nilpotent Lie groups of class 2. A group is called almost homogeneous if its automorphism group acts with at most 3 orbits. Several open problems about the existence of embeddings between almost homogeneous Heisenberg groups have been posed in a previous paper by the second author. Most of these problems are solved. Mathematics Subject Classification 2000:...

We consider the multi-marginal optimal transport of aligning several compactly supported marginals on Heisenberg group to minimize total cost, which we take be sum squared Carnot-Caratheodory distances from marginal points their barycenter. Under certain technical hypotheses, prove existence and uniqueness maps. also point out related open questions.