On quadratic Dehn functions.

DOI10.1007/s00209-004-0678-4zbMath1132.20021OpenAlexW1999504240MaRDI QIDQ706115

Enrico Leuzinger, Christophe Pittet

Publication date: 2 February 2005

Published in: Mathematische Zeitschrift (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s00209-004-0678-4

zbMATH Keywords

symmetric spacesisoperimetric inequalitiesRiemannian metricsDehn functionsfilling functionsHilbert modular groupsmetabelian polycyclic groupsquasi-geodesic foliationssimply connected solvable Lie groups

Mathematics Subject Classification ID

Geometric group theory (20F65) Discrete subgroups of Lie groups (22E40) Nilpotent and solvable Lie groups (22E25) Asymptotic properties of groups (20F69) Differential geometry of symmetric spaces (53C35)

Related Items

Filling inequalities for nilpotent groups through approximations. ⋮ Isoperimetry of nilpotent groups ⋮ Geometric presentations of Lie groups and their Dehn functions ⋮ Finiteness properties of arithmetic groups over function fields. ⋮ Dimension of asymptotic cones of Lie groups ⋮ The Dehn function of Baumslag's metabelian group. ⋮ The Dehn function of \(\text{SL}(n;\mathbb Z)\). ⋮ A Dehn function for Sp(2n, ℤ) ⋮ Filling invariants of stratified nilpotent Lie groups ⋮ The large-scale geometry of locally compact solvable groups

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Manifolds of nonpositive curvature
• Quadratic isometric functions of the Heisenberg groups. A combinatorial proof
• Filling in lattices of \(\mathbb{Q}\)-rank 1 and in solvable groups
• Isoperimetric inequalities and the homology of groups
• An isoperimetric inequality for the Heisenberg groups
• Isoperimetric inequalities for nilpotent groups.
• Exponential radicals of solvable Lie groups
• The isoperimetric profile of homogeneous Riemannian manifolds.
• Equivalence of geometric and combinatorial Dehn functions.
• An exhaustion of locally symmetric spaces by compact submanifolds with corners
• Isoperimetric inequalities for lattices in semisimple Lie groups of rank 2
• HYPERBOLICITY OF GROUPS WITH SUBQUADRATIC ISOPERIMETRIC INEQUALITY
• Dimension and Fundamental Groups of Asymptotic Cones
• Isoperimetric Inequalities in Nilpotent Groups
• Solvable groups with polynomial Dehn functions
• Injective Polynomial Maps are Automorphisms
• Coarse cohomology and index theory on complete Riemannian manifolds