A note on polyharmonic mappings
Daoud Bshouty, Stavros Evdoridis, Antti Rasila
TL;DR
This paper investigates properties of polyharmonic mappings, proving a Radó type theorem, exploring boundary function relationships, and demonstrating how to construct close-to-convex biharmonic mappings from convex harmonic mappings.
Contribution
It provides new theoretical results on polyharmonic mappings, including a Radó type theorem and methods to construct specific biharmonic mappings from harmonic ones.
Findings
No univalent polyharmonic mapping of the unit disk onto the entire complex plane exists.
Boundary functions of harmonic and biharmonic mappings are connected.
Close-to-convex biharmonic mappings can be derived from convex harmonic mappings.
Abstract
In this paper we prove a Rad\'o type result showing that there is no univalent polyharmonic mapping of the unit disk onto the whole complex plane. We also establish a connection between the boundary functions of harmonic and biharmonic mappings. Finally, we show how a close-to-convex biharmonic mapping can be constructed from a convex harmonic mapping.
Peer Reviews
No public reviews on file for this paper yet. If you reviewed it on a platform where reviews are public (OpenReview, ICLR, NeurIPS, ICML), you can paste yours below so the community can read it here.
Videos
No videos yet. Explain this paper in a talk, walkthrough, or lecture? Add one.