67 citations · 124 across the 33 of their papers we have counts for
25 papers · 1 filter
On the continuity of geodesically convex functions on Riemannian manifolds
Victor-Emmanuel Brunel, Pierre Pansu
In this short note, we prove that all geodesically convex functions defined on a Riemannian manifold are continuous in the interior of their domain. This is a folklore result, but…
Flat compactness of normal currents, and charges in Carnot groups
Antoine Julia, Pierre Pansu
We prove that the family of normal currents in the sense of Rumin in a Carnot group is compact in the flat topology. This result is obtained through a dual compactness argument for…
Averages and the -cohomology of Heisenberg groups
Pierre Pansu, Francesca Tripaldi
Averages are invariants defined on the cohomology of Lie groups. We prove that they vanish for abelian and Heisenberg groups. This result completes work by other authors a…
-Poincaré and Sobolev inequalities for differential forms in Euclidean spaces
Annalisa Baldi, Bruno Franchi, Pierre Pansu
In this paper, we prove Poincaré and Sobolev inequalities for differential forms in . The singular integral estimates that it is possible to use for , ,…
-Poincaré inequalities for differential forms on Euclidean spaces and Heisenberg groups
Annalisa Baldi, Bruno Franchi, Pierre Pansu
In this paper, we prove interior Poincar{é} and Sobolev inequalities in Euclidean spaces and in Heisenberg groups, in the limiting case where the exterior (resp. Rumin) differentia…
Poincar{é} and Sobolev inequalities for differential forms in Heisenberg groups
Annalisa Baldi, Bruno Franchi, Pierre Pansu
Poincar{é} and Sobolev inequalities for differential forms on Heisenberg balls, involving Rumin's differentials, are given. Furthermore, a global homotopy of Rumin's complex which…
Cup-products in L q,p -cohomology: discretization and quasi-isometry invariance
Pierre Pansu
We relate -cohomology of bounded geometry Riemannian manifolds to a purely metric space notion of -cohomology, packing cohomology. This implies quasi-isometry…
Asymptotic expansions of holonomy
Erlend Grong, Pierre Pansu
Given a principal bundle with a connection, we look for an asymptotic expansion of the holonomy of a loop in terms of its length. This length is defined relative to some Riemannian…
Submanifolds and differential forms on Carnot manifolds, after M. Gromov and M. Rumin
Pierre Pansu
The purpose of these notes is to explain parts of Gromov's survey of Carnot-Carathedory spaces, in the light of subsequent results of M. Rumin. Among the rich material provided by…
On the quasisymmetric Hölder-equivalence problem for Carnot groups
P Pansu
A variant of Gromov's H{ö}lder-equivalence problem, motivated by a pinching problem in Riemannian geometry, is discussed. A partial result is given. The main tool is a general coar…
Applications conformes {à} grande {é}chelle
Pierre Pansu
Roughly speaking, let us say that a map between metric spaces is large scale conformal if it maps packings by large balls to large quasi-balls with limited overlaps. This quasi-iso…
Gagliardo-Nirenberg Inequalities for Differential Forms in Heisenberg Groups
Annalisa Baldi, Bruno Franchi, Pierre Pansu
The L 1-Sobolev inequality states that the L n/(n--1)-norm of a compactly supported function on Euclidean n-space is controlled by the L 1-norm of its gradient. The generalization…
A discontinuous isoperimetric profile for a complete Riemannian manifold
Stefano Nardulli, Pierre Pansu
The first known example of a complete Riemannian manifold whose isoperimetric profile is discontinuous is given.
Lipschitz extensions of maps between Heisenberg groups
Zoltan Balogh, Urs Lang, Pierre Pansu
Let $\H^n$ be the Heisenberg group of topological dimension . We prove that if is odd, the pair of metric spaces $(\H^n, \H^n)$ does not have the Lipschitz extension prop…
Sard Property for the endpoint map on some Carnot groups
Enrico Le Donne, Richard Montgomery, Alessandro Ottazzi +2
In Carnot-Caratheodory or sub-Riemannian geometry, one of the major open problems is whether the conclusions of Sard's theorem holds for the endpoint map, a canonical map from an i…
Semianalyticity of isoperimetric profiles
Pierre Pansu, Renata Grimaldi, Stefano Nardulli
It is shown that, in dimensions , isoperimetric profiles of compact real analytic Riemannian manifolds are semi-analytic.
Differentiability of the isoperimetric profile and topology of analytic Riemannian manifolds
Renata Grimaldi, Stefano Nardulli, Pierre Pansu
We show that smooth isoperimetric profiles are exceptional for real analytic Riemannian manifolds. For instance, under some extra assumption, this can happen only on topological sp…
Flexibility of surface groups in classical groups
Inkang Kim, Pierre Pansu
We show that a surface group of high genus contained in a classical simple Lie group can be deformed to become Zariski dense, unless the Lie group is (resp. ,…
Density of Zariski density for surface groups
Inkang Kim, Pierre Pansu
We show that a surface group contained in a reductive real algebraic group can be deformed to become Zariski dense, unless its Zariski closure acts transitively on a Hermitian symm…
Bounded geometry, growth and topology
Renata Grimaldi, Pierre Pansu
We characterize functions which are growth types of Riemannian manifolds of bounded geometry.
Local quaternionic rigidity for complex hyperbolic lattices
Kim Inkang, Bruno Klingler, Pierre Pansu
Let be a lattice in the real simple Lie group . If is of rank at least 2 (respectively locally isomorphic to ) any unbounded morp…
Local rigidity in quaternionic hyperbolic space
Inkang Kim, Pierre Pansu
In this note, we study deformations of quaternionic hyperbolic lattices in larger quaternionic hyperbolic spaces and prove local rigidity results. On the other hand, surface groups…
Calibrations and isoperimetric profiles
Renata Grimaldi, Pierre Pansu
We equip many non compact non simply connected surfaces with smooth Riemannian metrics whose isoperimetric profile is smooth, a highly non generic property. The computation of the…
Lp-cohomology of symmetric spaces
Pierre Pansu
This is a short survey of Riemannian geometric applications of Lp-cohomology of thick spaces, p not equal to 2.