Logarithmic Potentials and Quasiconformal Flows on the Heisenberg Group

  title={Logarithmic Potentials and Quasiconformal Flows on the Heisenberg Group},
  author={Alex D. Austin},
  journal={arXiv: Classical Analysis and ODEs},
  • Alex D. Austin
  • Published 2017
  • Mathematics
  • arXiv: Classical Analysis and ODEs
  • Let $\mathbb{H}$ be the sub-Riemannian Heisenberg group. That $\mathbb{H}$ supports a rich family of quasiconformal mappings was demonstrated by Kor\'{a}nyi and Reimann using the so-called flow method. Here we supply further evidence of the flexible nature of this family, constructing quasiconformal mappings with extreme behavior on small sets. More precisely, we establish criteria to determine when a given logarithmic potential $\Lambda$ on $\mathbb{H}$ is such that there exists a… CONTINUE READING
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