On Convexity of Level Curves of Harmonic Functions in the Hyperbolic Plane

descriptionPublicationkeyboard_double_arrow_right Article , Other literature type 01 Mar 1992Publisher:JSTORJournal:Proceedings of the American Mathematical Society, volume 114, page 695 (issn: 0002-9939,

Copyright policy )

Authors: Papadimitrakis, M.;

doi: 10.2307/2159391 , 10.1090/s0002-9939-1992-1086339-3

On Convexity of Level Curves of Harmonic Functions in the Hyperbolic Plane

- Summary
- Subjects
- Metrics

Abstract

We prove that if two level curves of a harmonic function are convex in the hyperbolic disc then all intermediate level curves are also convex.

Keywords

Poincaré metric, convexity, Spherical and hyperbolic convexity, Convex sets in \(2\) dimensions (including convex curves), Harmonic, subharmonic, superharmonic functions in two dimensions

Impact byBIP!

	selected citations These citations are derived from selected sources. This is an alternative to the "Influence" indicator, which also reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).	8
	popularity This indicator reflects the "current" impact/attention (the "hype") of an article in the research community at large, based on the underlying citation network.	Average
	influence This indicator reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).	Average
	impulse This indicator reflects the initial momentum of an article directly after its publication, based on the underlying citation network.	Average