Alex D. Austin

collaborators

3 papers

math.DG2020

The contact mappings of a flat $(2, 3, 5)$ -distribution

Alex D. Austin

Let $Ω$ and $Ω^{'}$ be open subsets of a flat $(2, 3, 5)$ -distribution. We show that a $C^{1}$ -smooth contact mapping $f : Ω \to Ω^{'}$ is a $C^{\infty}$ -smooth contact mapping. Ultimately, thi…

math.AP2017

A new proof of the $C^{\infty}$ regularity of $C^{2}$ conformal mappings on the Heisenberg group

Alex D. Austin, Jeremy T. Tyson

We give a new proof for the $C^{\infty}$ regularity of $C^{2}$ smooth conformal mappings of the sub-Riemannian Heisenberg group. Our proof avoids any use of nonlinear potential theory…

math.CA2017

Logarithmic Potentials and Quasiconformal Flows on the Heisenberg Group

Alex D. Austin

Let $H$ be the sub-Riemannian Heisenberg group. That $H$ supports a rich family of quasiconformal mappings was demonstrated by Korányi and Reimann using the so-ca…

The contact mappings of a flat (2,3,5)-distribution

A new proof of the C∞ regularity of C2 conformal mappings on the Heisenberg group

Logarithmic Potentials and Quasiconformal Flows on the Heisenberg Group

The contact mappings of a flat $(2, 3, 5)$ -distribution

A new proof of the $C^{\infty}$ regularity of $C^{2}$ conformal mappings on the Heisenberg group