Pavlovic's theorem in space
Kari Astala, Vesna Manojlovic
TL;DR
This paper explores higher-dimensional analogs of Pavlovic's theorem, extending the understanding of harmonic quasiconformal mappings beyond the disk to more complex spaces.
Contribution
It introduces higher-dimensional counterparts to Pavlovic's theorem, broadening the scope of harmonic quasiconformal mapping theory.
Findings
Harmonic quasiconformal mappings in higher dimensions exhibit bi-Lipschitz properties under certain conditions.
Extension of Pavlovic's theorem to higher-dimensional spaces.
New theoretical framework for analyzing harmonic quasiconformal maps in complex spaces.
Abstract
We study higher dimensional counterparts to the well-known theorem of Pavlovic \cite{pa3}, that every harmonic quasiconformal mapping of the disk is bi-Lipschitz.
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Taxonomy
TopicsHolomorphic and Operator Theory · Advanced Banach Space Theory · Analytic and geometric function theory