On harmonic quasiconformal quasi-isometries
Miodrag Mateljevi\'c, Matti Vuorinen
TL;DR
This paper investigates conditions under which harmonic maps are Lipschitz continuous relative to quasihyperbolic metrics, establishing that harmonic quasiconformal maps possess this property.
Contribution
It proves that harmonic quasiconformal maps are Lipschitz with respect to quasihyperbolic metrics, advancing understanding of their regularity properties.
Findings
Harmonic quasiconformal maps are Lipschitz w.r.t. quasihyperbolic metrics
Identifies conditions ensuring Lipschitz continuity of harmonic maps
Contributes to the theory of harmonic quasiconformal mappings
Abstract
The purpose of this paper is to explore conditions which guarantee Lipschitz-continuity of harmonic maps w.r.t. quasihyperbolic metrics. For instance, we prove that harmonic quasiconformal maps are Lipschitz w.r.t. quasihyperbolic metrics.
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Taxonomy
TopicsAnalytic and geometric function theory · Geometric Analysis and Curvature Flows · Nonlinear Partial Differential Equations