Convexity in Multivalued Harmonic Functions

Abstract

We investigate variants of a Three Circles type Theorem in the context of \mathcal{Q}-valued functions. We prove some convexity inequalities related to the L^{2} growth function in the \mathcal{Q}-valued settings. Optimality of these inequalities and comparsion to the case of real valued harmonic functions is also discussed.

arXiv comment16 pages. Real Analysis Exchange. Vol. 47(2) 2022 pp. 1-19