Croissance des boules et des géodésiques fermées dans les nilvariétés
From MaRDI portal
Publication:4747187
DOI10.1017/S0143385700002054zbMath0509.53040OpenAlexW2074864316MaRDI QIDQ4747187
Publication date: 1983
Published in: Ergodic Theory and Dynamical Systems (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.1017/s0143385700002054
nilpotent groupnilmanifoldclosed geodesicslattice point problemfinitely generated discrete groupvolume of balls
Geodesics in global differential geometry (53C22) Global Riemannian geometry, including pinching (53C20) Discontinuous groups of transformations (57S30)
Related Items
Quadratic divergence of geodesics in CAT(0) spaces ⋮ Analysis on nilpotent groups ⋮ QUASI-ISOMETRY INVARIANTS AND ASYMPTOTIC CONES ⋮ How smooth is quantum complexity? ⋮ CAT(0) cube complexes with flat hyperplanes ⋮ Diophantine properties of nilpotent Lie groups ⋮ Connectedness of spheres in Cayley graphs ⋮ On value distributions for quasimeromorphic mappings on \(\mathbb H\)-type Carnot groups ⋮ Speed of convergence in first passage percolation and geodesicity of the average distance ⋮ On the logarithmic coarse structures of Lie groups and hyperbolic spaces ⋮ Lifshitz asymptotics for percolation Hamiltonians ⋮ Asymptotic behavior of the Riemannian Heisenberg group and its horoboundary ⋮ Amenability, locally finite spaces, and bi-Lipschitz embeddings ⋮ Asymptotic cones of HNN extensions and amalgamated products. ⋮ Asymptotic shapes for stationary first passage percolation on virtually nilpotent groups ⋮ Lipschitz Carnot-Carathéodory structures and their limits ⋮ Cone‐equivalent nilpotent groups with different Dehn functions ⋮ A primer on Carnot groups: homogenous groups, Carnot-Carathéodory spaces, and regularity of their isometries ⋮ Subsets of virtually nilpotent groups with the SBM property ⋮ Asymptotic cones and Assouad-Nagata dimension ⋮ Dimension of asymptotic cones of Lie groups ⋮ Crystallographic Helly groups ⋮ Hilbert volume in metric spaces. I ⋮ Extremal length for quasiregular mappings on Heisenberg groups. ⋮ Rational growth and degree of commutativity of graph products ⋮ Volume of spheres in doubling metric measured spaces and in groups of polynomial growth ⋮ On problems related to growth, entropy, and spectrum in group theory ⋮ The Heisenberg group is pan-rational ⋮ Large deviation and the tangent cone at infinity of a crystal lattice ⋮ Growth behaviors in the range \(e^{r^\alpha}\). ⋮ Folner sets of alternate directed groups ⋮ Ultrarigid tangents of sub-Riemannian nilpotent groups ⋮ The asymptotic density of finite-order elements in virtually nilpotent groups. ⋮ Expected depth of random walks on groups ⋮ Groups acting on semimetric spaces and quasi-isometries of monoids ⋮ Central limit theorem for exponentially quasi-local statistics of spin models on Cayley graphs ⋮ Laws of the iterated logarithm on covering graphs with groups of polynomial volume growth ⋮ Limit elements in the configuration algebra for a cancellative monoid ⋮ On pairs of metrics invariant under a cocompact action of a group ⋮ Multivariable averaging on sparse sets ⋮ Profil isopérimétrique, métriques périodiques et formes d'équilibre des cristaux ⋮ Equidistribution of dense subgroups on nilpotent Lie groups ⋮ Filling invariants of stratified nilpotent Lie groups ⋮ On the escape rate of geodesic loops in an open manifold with nonnegative Ricci curvature ⋮ On effective Birkhoff's ergodic theorem for computable actions of amenable groups ⋮ Sub-Finsler horofunction boundaries of the Heisenberg group ⋮ Entropy and drift for word metrics on relatively hyperbolic groups ⋮ The homeomorphism problem for closed 3-manifolds ⋮ Asymptotic cones and boundaries of CAT(0) spaces ⋮ Translation-like actions of nilpotent groups ⋮ Quasi-isometric rigidity for graphs of virtually free groups with two-ended edge groups ⋮ Isomorphisms between spaces of Lipschitz functions ⋮ \(L^p\) estimates of Schrödinger operators on nilpotent groups ⋮ The asymptotic shape theorem for the frog model on finitely generated abelian groups ⋮ Gradings on Lie algebras, systolic growth, and cohopfian properties of nilpotent groups ⋮ Almost additive entropy ⋮ On groups with locally compact asymptotic cones ⋮ A cornucopia of Carnot groups in low dimensions ⋮ Quasi-conformal maps on model filiform groups ⋮ Exponential radicals of solvable Lie groups ⋮ Polynomial growth harmonic functions on groups of polynomial volume growth ⋮ Explicit universal minimal constants for polynomial growth of groups ⋮ On the speed of convergence to the asymptotic cone for non-singular nilpotent groups ⋮ Rational growth in torus bundle groups of odd trace ⋮ Integrable measure equivalence for groups of polynomial growth ⋮ Hierarchically hyperbolic spaces. I: Curve complexes for cubical groups
Cites Work
- Geometric properties of Heisenberg-type groups
- Groups of polynomial growth and expanding maps. Appendix by Jacques Tits
- Riemannian nilmanifolds attached to Clifford modules
- Nilpotent Lie groups: Structure and applications to analysis
- Least action principle, heat propagation and subelliptic estimates on certain nilpotent groups
- Normal and integral currents
- Orbits of Families of Vector Fields and Integrability of Distributions
- The Degree of Polynomial Growth of Finitely Generated Nilpotent Groups