Quasiregular maps and the conductivity equation in the Heisenberg group

Abstract

Abstract. We show that the interplay between the planar Beltrami equation governing quasiconformal and quasiregular mappings and Calderón's conductivity equation in impedance tomography admits a counterpart in the setting of the first Heisenberg group equipped with its canonical sub-Riemannian structure.

Maxwell’s Equations in Anisotropic Media and Carnot Groups as Variational Limits

“…In fact, Maxwell's equations in Carnot groups have been introduced in order to carry on the investigation of peculiar features of the geometry of the groups. Nevertheless, we want to mention that in the first Heisenberg group H 1 equations (1.4) and (1.5) arise in the study of quasiconformal or quasiregular maps in H 1 , precisely as classical Maxwell's equations appear in quasiconformal map theory in the Euclidean setting (see [23], [1]).…”