Quasiconformal mappings in the hyperbolic Heisenberg group and a lifting theorem
Ioannis D. Platis
TL;DR
This paper investigates smooth contact quasiconformal mappings in the hyperbolic Heisenberg group, establishing a lifting theorem that connects symplectic quasiconformal maps of the hyperbolic plane to circles-preserving quasiconformal maps in the group.
Contribution
It introduces a lifting theorem that links symplectic quasiconformal mappings of the hyperbolic plane to circles-preserving quasiconformal mappings in the hyperbolic Heisenberg group.
Findings
Established a lifting theorem for quasiconformal mappings
Connected symplectic quasiconformal maps to circle-preserving maps
Enhanced understanding of quasiconformal mappings in hyperbolic geometry
Abstract
A study of smooth contact quasiconformal mappings of the hyperbolic Heisenberg group is presented in this paper. Our main result is a Lifting Theorem; according to this, a symplectic quasiconformal mapping of the hyperbolic plane can be lifted to a circles preserving quasiconformal mapping of the hyperbolic Heisenberg group.
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Taxonomy
TopicsGeometric Analysis and Curvature Flows · Analytic and geometric function theory · Advanced Algebra and Geometry