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

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.

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)