Three-spheres theorem for harmonic functions (non-concentric case)
Analysis of PDEs
2026-04-07 v1 Complex Variables
Abstract
A direct analog of Hadamard's three-circle theorem is obtained for harmonic functions (in weighted L^2-norm) in case of (n-1)-dimensional non-concentric spheres in R^n. The result extends the concentric case to correlated non-concentric, non-touching spheres via an inversion technique. Applications to propagation of smallness and uniqueness for harmonic functions are given.
Keywords
Cite
@article{arxiv.2604.03442,
title = {Three-spheres theorem for harmonic functions (non-concentric case)},
author = {Norair U. Arakelian and Norayr Matevosyan},
journal= {arXiv preprint arXiv:2604.03442},
year = {2026}
}
Comments
15 pages. Originally written as master's thesis, Yerevan State University, 1999. Sections 1-4 published in Izv. Nats. Akad. Nauk Armenii Mat. 34 (1999), no. 3, 5-13. This expanded version includes additional uniqueness results (Sections 5-6)