A proof of the Khavinson conjecture

DOI10.1007/s00208-020-01983-wzbMath1472.31007arXiv1909.00635OpenAlexW3014692360WikidataQ123275437 ScholiaQ123275437MaRDI QIDQ2035589

Cong Wen Liu

Publication date: 25 June 2021

Published in: Mathematische Annalen (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1909.00635

zbMATH Keywords

harmonic functionsKhavinson conjecture

Mathematics Subject Classification ID

Harmonic, subharmonic, superharmonic functions in higher dimensions (31B05) Laplace operator, Helmholtz equation (reduced wave equation), Poisson equation (35J05)

Related Items (5)

A Khavinson type conjecture for hyperbolic harmonic functions on the unit ball ⋮ Schwarz-Pick lemma for harmonic and hyperbolic harmonic functions ⋮ Khavinson problem for hyperbolic harmonic mappings in Hardy space ⋮ Some sharp Schwarz-Pick type estimates and their applications of harmonic and pluriharmonic functions ⋮ Unnamed Item

Cites Work

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• Solution to the Khavinson problem near the boundary of the unit ball
• Sharp pointwise estimates for directional derivatives of harmonic functions in a multidimensional ball
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• A proof of the Khavinson conjecture in \(\mathbb{R}^3\)
• Positivity and the convolution structure for Jacobi series
• Banach algebras for Jacobi series and positivity of a kernel
• An Extremal Problem for Harmonic Functions in the Ball
• A proof of Khavinson's conjecture in R4

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