@article{ee6fb6f5996c4c81971ae075b630ca6d,
title = "On the existence of harmonic mappings between doubly connected domains",
abstract = "While the existence of conformal mappings between doubly connected domains is characterized by their conformal moduli, no such characterization is available for harmonic diffeomorphisms. Intuitively, one expects their existence if the domain is not too thick compared to the codomain. We make this intuition precise by showing that for a Dini-smooth doubly connected domain Ω∗ there exists a I > 0 such that for every doubly connected domain Ω with ModΩ∗ < ModΩ < ModΩ∗ I there exists a harmonic diffeomorphism from Ω onto Ω∗.",
keywords = "2010 Mathematics subject classification: Primary 31A05, 30C20, Secondary 58E20",
author = "Kovalev, {Leonid V.} and Liulan Li",
note = "Funding Information: This work was completed during the visit of L.L. to Syracuse University. She thanks the university for its hospitality. The visit and the research of L.L. was supported by CSC of China (Grant no. 201308430274). The research was also supported by NSF of China (Grant nos 11201130 and 11571216), Hunan Provincial Natural Science Foundation of China (Grant no. 14JJ1012) and a construct programme of the key discipline in Hunan province. The research of L.V.K. was supported by the National Science Foundation grant DMS-1362453. The authors thank the referee for suggesting corrections and additional references. Publisher Copyright: {\textcopyright} Royal Society of Edinburgh 2018.",
year = "2018",
month = jun,
day = "1",
doi = "10.1017/S0308210517000506",
language = "English (US)",
volume = "148",
pages = "619--628",
journal = "Proceedings of the Royal Society of Edinburgh Section A: Mathematics",
issn = "0308-2105",
publisher = "Cambridge University Press",
number = "3",
}