Dual topology of diamond groups.
Duality of Hodge numbers of compact complex nilmanifolds
A compact K¨ahlerian manifoldM of dimension n satisfies hp,q(M) = hq,p(M) for each p, q.However, a compact complex manifold does not satisfy the equations in general. In this paper, we consider duality of Hodge numbers of compact complex nilmanifolds.
Einstein Metrics on solvable groups.
Équations aux différences associées à des groupes, fonctions représentatives.
Inspiré par un travail de J.-P. Bézivin et F. Gramain sur les systèmes d’équations aux différences, on caractérise les sous-groupes d’un groupe de Lie réel (resp. complexe) , pour lesquels toute fonction continue (resp. entière) telle que l’ensemble des -translatées engendrent un -espace vectoriel de dimension finie, engendrent aussi un -espace vectoriel de dimension finie par - translation. On fait le lien avec les systèmes d’équations aux différences à coefficients constants.
Equivalence of weak and viscosity solutions to the -Laplace equation in the Heisenberg group.
Estimates for derivatives of the Green functions on homogeneous manifolds of negative curvature.
Estimates for the mixed derivatives of the Green functions on homogeneous manifolds of negative curvature.
Estimates for the Poisson kernel on higher rank NA groups
We obtain an estimate for the Poisson kernel for the class of second order left-invariant differential operators on higher rank NA groups.
Estimates for the Poisson kernels and a Fatou type theorem applications to analysis on Siegel domains
This is a short description of some results obtained by Ewa Damek, Andrzej Hulanicki, Richard Penney and Jacek Zienkiewicz. They belong to harmonic analysis on a class of solvable Lie groups called NA. We apply our results to analysis on classical Siegel domains.
Estimates for the Poisson kernels and their derivatives on rank one NA groups
For rank one solvable Lie groups of the type NA estimates for the Poisson kernels and their derivatives are obtained. The results give estimates on the Poisson kernel and its derivatives in a natural parametrization of the Poisson boundary (minus one point) of a general homogeneous, simply connected manifold of negative curvature.
Example of a six-dimensional LCK solvmanifold
The purpose of this paper is to prove that there exists a lattice on a certain solvable Lie group and construct a six-dimensional locally conformal Kähler solvmanifold with non-parallel Lee form.
Exemples de feuilletages de Lie
Nous donnons des exemples de feuilletages de Lie sur une variété compacte qui ne se déforment pas en des feuilletages de Lie à holonomie discrète.
Existence of generalized symmetric Riemannian spaces with solvable isometry group
Existence of solutions for transversally elliptic left invariant differential operators on nilpotent Lie groups
Extensions of representations of analytic solvable groups.
Feuilletages de Lie résolubles
Four dimensional symplectic Lie algebras.
Fourier transform of Schwartz functions on the Heisenberg group
Let H₁ be the 3-dimensional Heisenberg group. We prove that a modified version of the spherical transform is an isomorphism between the space 𝓢ₘ(H₁) of Schwartz functions of type m and the space 𝓢(Σₘ) consisting of restrictions of Schwartz functions on ℝ² to a subset Σₘ of the Heisenberg fan with |m| of the half-lines removed. This result is then applied to study the case of general Schwartz functions on H₁.
Fourier-Stieltjes algebras of compact extensions of nilpotent groups.
Funktionenalgebren auf Bahnen nilpotenter Gruppen