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We consider contact manifolds equipped with Carnot-Caratheodory metrics, and show that the Rumin complex is respected by Sobolev mappings: Pansu pullback induces a chain mapping between the smooth Rumin complex and the distributional Rumin complex. As a consequence, the Rumin flat complex -- the analog of the Whitney flat complex in the setting of contact manifolds -- is bilipschitz invariant. We also show that for Sobolev mappings between general Carnot groups, Pansu pullback induces a chain mapping when restricted to a certain differential ideal of the de Rham complex. Both results are applications of the Pullback Theorem from our previous paper.
We give a new CR invariant treatment of the bigraded Rumin complex and related cohomology groups via differential forms. We also prove related Hodge decomposition theorems. Among many applications, we give a sharp upper bound on the dimension of the
In this paper an alternative definition of the Rumin complex $(E_0^bullet,d_c)$ is presented, one that relies on a different concept of weights of forms. In this way, the Rumin complex can be constructed on any nilpotent Lie group equipped with a Car
We extend Federers coarea formula to mappings $f$ belonging to the Sobolev class $W^{1,p}(R^n;R^m)$, $1 le m < n$, $p>m$, and more generally, to mappings with gradient in the Lorentz space $L^{m,1}(R^n)$. This is accomplished by showing that the grap
This is an overview article. In his Habilitationsvortrag, Riemann described infinite dimensional manifolds parameterizing functions and shapes of solids. This is taken as an excuse to describe convenient calculus in infinite dimensions which allows
We consider mappings $f:Gsupset Urightarrow G$ where $G$ and $G$ are Carnot groups and U is an open subset. We prove a number of new structural results for Sobolev (in particular quasisymmetric) mappings, establishing (partial) rigidity or (partial)