Harmonic extensions of quasisymmetric maps
Anestis Fotiadis
TL;DR
This paper investigates the Dirichlet problem for harmonic maps between hyperbolic planes, focusing on cases where the boundary map's Euclidean harmonic extension is quasiconformal, to understand the extension properties and regularity.
Contribution
It provides new insights into harmonic extensions of boundary maps that are quasiconformal, expanding understanding of harmonic map regularity in hyperbolic geometry.
Findings
Harmonic maps extend quasiconformal boundary maps under certain conditions
Characterization of harmonic extensions in hyperbolic planes
Conditions ensuring regularity of harmonic maps
Abstract
We study the Dirichlet problem for harmonic maps between hyperbolic planes, under the assumption that the Euclidean harmonic extension of the boundary map is quasiconformal.
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Taxonomy
TopicsAnalytic and geometric function theory · Geometric Analysis and Curvature Flows · Geometric and Algebraic Topology