Ben Warhurst

CONTACT AND PANSU DIFFERENTIABLE MAPS ON CARNOT GROUPS

The equivalence between contact and Pansu differentiable maps on Carnot groups is established within the class of maps that are C 1 with respect to the ambient Euclidean structure.

Invariants and Infinitesimal Transformations for Contact Sub-Lorentzian Structures on 3-Dimensional Manifolds

In this article we develop some elementary aspects of a theory of symmetry in sub-Lorentzian geometry. First of all we construct invariants characterizing isometric classes of sub-Lorentzian contact 3 manifolds. Next we characterize vector fields which generate isometric and conformal symmetries in general sub-Lorentzian manifolds. We then focus attention back to the case where the underlying manifold is a contact 3 manifold and more specifically when the manifold is also a Lie group and the structure is left-invariant.

A Liouville Type Theorem for Carnot Groups: A Case Study

L. Capogna and M. Cowling showed that if

Sub-Riemannian vs. Euclidean dimension comparison and fractal geometry on Carnot groups

\phi

Contact and 1-quasiconformal maps on Carnot groups

is 1-quasiconformal on an open subset of a Carnot group G, then composition with

Algebraic prolongation and rigidity of Carnot groups

\phi

Tanaka prolongation of free Lie algebras

preserves Q-harmonic functions, where Q denotes the homogeneous dimension of G. Then they combine this with a regularity theorem for Q-harmonic functions to show that

Contact and quasiconformal mappings on real model filiform groups

\phi

ULTRARIGID TANGENTS OF SUB-RIEMANNIAN NILPOTENT GROUPS

is in fact

Gromov's dimension comparison problem on Carnot groups

C^\infty