Access the full text.
Sign up today, get DeepDyve free for 14 days.
S. Gersten, D. Holt, T. Riley (2002)
Isoperimetric inequalities for nilpotent groupsGeometric & Functional Analysis GAFA, 13
J. Burillo (1999)
Dimension and Fundamental Groups of Asymptotic ConesJournal of the London Mathematical Society, 59
W. Ballmann (1985)
Manifolds of non positive curvature
D. Osin (2002)
Exponential Radicals of Solvable Lie GroupsJournal of Algebra, 248
Cornelia Drutu (2001)
Filling in solvable groups and in lattices in semisimple groupsTopology, 43
S. Gersten (1993)
Geometric Group Theory: Isoperimetric and Isodiametric Functions of Finite Presentations
J. Alonso (1990)
INEGALITES ISOPERIMETRIQUES ET QUASI-ISOMETRIES, 311
W. Rudin (1995)
Injective Polynomial Maps Are AutomorphismsAmerican Mathematical Monthly, 102
G. Arzhantseva, D. Osin (2002)
Solvable groups with polynomial Dehn functionsTransactions of the American Mathematical Society, 354
C. Druţu (1998)
REMPLISSAGE DANS DES RESEAUX DE Q-RANG 1 ET DANS DES GROUPES RESOLUBLESPacific Journal of Mathematics, 185
A. Ol'shanskii (1991)
Hyperbolicity of Groups with Subquadratic isoperimetric inequalityInt. J. Algebra Comput., 1
C. Pittet (1997)
Isoperimetric Inequalities in Nilpotent GroupsJournal of the London Mathematical Society, 55
E. Leuzinger, C. Pittet (1996)
Isoperimetric inequalities for lattices in semisimple lie groups of rank 2Geometric & Functional Analysis GAFA, 6
D. Epstein (1992)
Word processing in groups
Benoı̂t Chaluleau (2003)
Problème du mot, invariants de quasi-isométrie pour les groupes
C. Pittet (2000)
The isoperimetric profile of homogeneous Riemannian manifoldsJournal of Differential Geometry, 54
Daniel Allcock (1998)
An isoperimetric inequality for the Heisenberg groupsGeometric & Functional Analysis GAFA, 8
A. Olshanskii, M. Sapir (1999)
Quadratic isometric functions of the Heisenberg groups. A combinatorial proofJournal of Mathematical Sciences, 93
E. Heintze (1974)
On homogeneous manifolds of negative curvatureMathematische Annalen, 211
Graham Niblo, M. Roller, J. Cassels (1993)
Geometric Group Theory: Asymptotic Invariants of Infinite Groups, M. Gromov
J. Burillo (1995)
Equivalence of Geometric and Combinatorial Dehn FunctionsarXiv: Group Theory
E. Leuzinger (1995)
An exhaustion of locally symmetric spaces by compact submanifolds with cornersInventiones mathematicae, 121
G. Baumslag, Charles Miller, H. Short (1993)
Isoperimetric inequalities and the homology of groupsInventiones mathematicae, 113
We confirm with new examples that “Solvable groups of high ℝ-rank are expected to satisfy a polynomial isoperimetric inequality” ([Gro93] 5A9). To that end we study invariant quasi-geodesic foliations in simply connected solvable Lie groups, endowed with left-invariant Riemannian metrics, whose leaves are isometric to closed subgroups. We establish a decomposition theorem which implies upper bounds on the Dehn (or filling) function (of loops by disks) of the solvable group in terms of the Dehn functions of the leaves. We obtain examples of metabelian polycyclic groups with exponential growth and quadratic Dehn functions. We also deduce that the horospheres in SL(4,ℝ)/SO(4,ℝ) which bound an invariant core for SL(4, ℤ) and that the horospheres which bound an invariant core for Hilbert modular groups in [InlineMediaObject not available: see fulltext.] have quadratic filling functions. The main theorem also applies to some solvable Lie groups which are not quasi-isometric to horospheres in symmetric spaces.
Mathematische Zeitschrift – Springer Journals
Published: May 6, 2004
Read and print from thousands of top scholarly journals.
Already have an account? Log in
Bookmark this article. You can see your Bookmarks on your DeepDyve Library.
To save an article, log in first, or sign up for a DeepDyve account if you don’t already have one.
Copy and paste the desired citation format or use the link below to download a file formatted for EndNote
Access the full text.
Sign up today, get DeepDyve free for 14 days.
All DeepDyve websites use cookies to improve your online experience. They were placed on your computer when you launched this website. You can change your cookie settings through your browser.