Three-spheres theorem for harmonic functions (non-concentric case)

Norair U. Arakelian; Norayr Matevosyan

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arXiv · 2604.03442

Three-spheres theorem for harmonic functions (non-concentric case)

Norair U. Arakelian·Norayr Matevosyan

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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.

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Norair U. Arakelian, Norayr Matevosyan. 2026-04-03. Three-spheres theorem for harmonic functions (non-concentric case). https://arxiv.org/abs/2604.03442

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