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Displaying 181 – 200 of 244

Regularity of minimizers of the calculus of variations in Carnot groups via hypoellipticity of systems of Hörmander type

Luca Capogna, Nicola Garofalo (2003)

Journal of the European Mathematical Society

We prove the hypoellipticity for systems of Hörmander type with constant coefficients in Carnot groups of step 2. This result is used to implement blow-up methods and prove partial regularity for local minimizers of non-convex functionals, and for solutions of non-linear systems which appear in the study of non-isotropic metric structures with scalings. We also establish estimates of the Hausdorff dimension of the singular set.

Remarks on Hodge numbers and invariant complex structures of compact nilmanifolds

Takumi Yamada (2016)

Complex Manifolds

If N is a simply connected real nilpotent Lie group with a Γ-rational complex structure, where Γ is a lattice in N, then [...] for each s, t.We study relations between invariant complex structures and Hodge numbers of compact nilmanifolds from a viewpoint of Lie algberas.

Représentations du groupe de Heisenberg dans les espaces de (0,q)-formes.

J. Carmona (1973)

Mathematische Annalen

Représentations unitaires des groupes de Lie résolubles

Michèle Vergne (1973/1974)

Séminaire Bourbaki

Ricci Curvature of Left Invariant Metrics on Solvable Unimodular Lie Groups.

Isabel Dotti Miatello (1982)

Mathematische Zeitschrift

Ricci-flat left-invariant Lorentzian metrics on 2-step nilpotent Lie groups

Mohammed Guediri, Mona Bin-Asfour (2014)

Archivum Mathematicum

The purpose of this paper is to investigate Ricci-flatness of left-invariant Lorentzian metrics on 2-step nilpotent Lie groups. We first show that if $〈,〉$ is a Ricci-flat left-invariant Lorentzian metric on a 2-step nilpotent Lie group $N$ , then the restriction of $〈,〉$ to the center of the Lie algebra of $N$ is degenerate. We then characterize the 2-step nilpotent Lie groups which can be endowed with a Ricci-flat left-invariant Lorentzian metric, and we deduce from this that a Heisenberg Lie group $H_{2 n + 1}$ can be...

Riesz means on Lie groups and riemannian manifolds of nonnegative curvature

Georgios Alexopoulos, Noël Lohoué (1994)

Bulletin de la Société Mathématique de France

Semicharacters and Solvable Lie Croups.

Niels Vigand Pedersen (1980)

Mathematische Annalen

Semigroups in lattices of solvable Lie groups.

do Rocio, Osvaldo Germano, San Martin, Luiz A.B. (1995)

Journal of Lie Theory

Separation of unitary representations of $ℝ \times ℝ^{d}$ .

Abdelmoula, Lobna, Arnal, Didier, Selmi, Mohamed (2004)

Journal of Lie Theory

Sharp Inequalities for Weyl Operators and Heisenberg Groups.

Abel Klein, Bernard Russo (1978)

Mathematische Annalen

Sharp pointwise estimate for the kernels of the semigroup generated by sums of even powers of vector fields on homogeneous groups

Waldemar Hebisch (1989)

Studia Mathematica

Some oscillatory integrals and their applications

E. M. Stein (1984/1985)

Séminaire Équations aux dérivées partielles (Polytechnique)

Some properties of Carnot-Carathéodory balls in the Heisenberg group

Roberto Monti (2000)

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni

Using the exact representation of Carnot-Carathéodory balls in the Heisenberg group, we prove that: 1. $|\nabla_{H^{n}} d (z, t)| = 1$ in the classical sense for all $(z, t) \in H^{n}$ with $z \neq 0$ , where $d$ is the distance from the origin; 2. Metric balls are not optimal isoperimetric sets in the Heisenberg group.

Special Functions and Infinite-dimensional Representations of Lie Groups.

P. Feinsilver, R. Schott (1990)

Mathematische Zeitschrift

Spectral multipliers on metabelian groups.

Waldemar Hebisch (2000)

Revista Matemática Iberoamericana

Let G be a Lie group, Xj right invariant vector fields on G, which generate (as a Lie algebra) the Lie algebra of G,L = -Σ Xj2.(...) In this paper we consider L1(G) boundedness of F(L) for (some) metabelian G and a distinguished L on G. Of the main interest is that the group is of exponential growth, and possibly higher rank. Previously positive results about higher rank groups were only about Iwasawa type groups. Also, our groups may be unimodular, so it is the second positive result (after [13])...

Spherical means on the Heisenberg group and a restriction theorem for the symplectic Fourier transform.

Sundaram Thangavelu (1991)

Revista Matemática Iberoamericana

The aim of this paper is to study mean value operators on the reduced Heisenberg group Hn/Γ, where Hn is the Heisenberg group and Γ is the subgroup {(0,2πk): k ∈ Z} of Hn.

Square-integrable representations mod $Z$ of unipotent groups

G. Van Dijk (1974)

Compositio Mathematica

Stein Quotients of Connected Complex Lie Groups.

Dennis M. Snow (1985)

Manuscripta mathematica

Strichartz inequalities for the Schrödinger equation with the full Laplacian on the Heisenberg group

Giulia Furioli, Alessandro Veneruso (2004)

Studia Mathematica

We prove Strichartz inequalities for the solution of the Schrödinger equation related to the full Laplacian on the Heisenberg group. A key point consists in estimating the decay in time of the $L^{\infty}$ norm of the free solution; this requires a careful analysis due also to the non-homogeneous nature of the full Laplacian.

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