Add to ORKGLet $N\subset GL(n,R)$ be the group of upper triangular matrices with $1$s on the diagonal, equipped with the standard Carnot group structure. We show that quasiconformal homeomorphisms between open subsets of $N$, and more generally Sobolev mappings with nondegenerate Pansu differential, are rigid when $n \geq 4$; this settles the Regularity Conjecture for such groups. This result is deduced from a rigidity theorem for the manifold of complete flags in $R^n$. Similar results also hold in the complex and quaternion cases.Comment: Added citations to earlier work which had been overlooked in the previous version of the pape
We introduce the notion of a point on a locally closed subset of a symplectic manifold being "locall...
We prove a rigidity type result for stratified nilpotent Lie algebras which gives a positive answer ...
We show that if f is a 1-quasiconformal map defined on an open subset of a Carnot group G, then comp...
In this article we consider contact mappings on Carnot groups. Namely, we are interested in those ma...
We study the regularity of a conjugacy $H$ between a hyperbolic toral automorphism $A$ and its smoot...
We prove quantitative stability of isometries on the first Heisenberg group with sub-Riemannian geom...
Cohomological rigidity theorems (with Banach coefficients) for some matrix groupsG over general ring...
For i = 1, 2, let Gi be cocompact groups of isometries of hyperbolic space Hn of real dimension n, n...
An action of a group Г on a manifold M is a homomorphism ρ from Г to Diff(M). ρo is locally rigid i...
An n-dimensional convex polytope is called simple if at each vertex exactly n facets (codimension on...
International audienceFor a G-variety X with an open orbit, we define its boundary ∂X as the complem...
We initiate a study of the topological group PPQI(G,H) of pattern-preserving quasi-isometries for G ...
We show that if the image of a Legendrian submanifold under a contact homeomorphism (i.e. a homeomor...
ABSTRACT. We say that a Lie algebra g quasi-state rigid if every Ad-invariant Lie quasi-state on it ...
A question whether sufficiently regular manifold automorphisms may have wandering domains with contr...
We introduce the notion of a point on a locally closed subset of a symplectic manifold being "locall...
We prove a rigidity type result for stratified nilpotent Lie algebras which gives a positive answer ...
We show that if f is a 1-quasiconformal map defined on an open subset of a Carnot group G, then comp...
In this article we consider contact mappings on Carnot groups. Namely, we are interested in those ma...
We study the regularity of a conjugacy $H$ between a hyperbolic toral automorphism $A$ and its smoot...
We prove quantitative stability of isometries on the first Heisenberg group with sub-Riemannian geom...
Cohomological rigidity theorems (with Banach coefficients) for some matrix groupsG over general ring...
For i = 1, 2, let Gi be cocompact groups of isometries of hyperbolic space Hn of real dimension n, n...
An action of a group Г on a manifold M is a homomorphism ρ from Г to Diff(M). ρo is locally rigid i...
An n-dimensional convex polytope is called simple if at each vertex exactly n facets (codimension on...
International audienceFor a G-variety X with an open orbit, we define its boundary ∂X as the complem...
We initiate a study of the topological group PPQI(G,H) of pattern-preserving quasi-isometries for G ...
We show that if the image of a Legendrian submanifold under a contact homeomorphism (i.e. a homeomor...
ABSTRACT. We say that a Lie algebra g quasi-state rigid if every Ad-invariant Lie quasi-state on it ...
A question whether sufficiently regular manifold automorphisms may have wandering domains with contr...
We introduce the notion of a point on a locally closed subset of a symplectic manifold being "locall...
We prove a rigidity type result for stratified nilpotent Lie algebras which gives a positive answer ...
We show that if f is a 1-quasiconformal map defined on an open subset of a Carnot group G, then comp...