Growth properties of superharmonic functions along rays

Gardiner, Stephen

doi:10.1090/S0002-9939-99-05197-7

Growth properties of superharmonic functions along rays
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Proc. Amer. Math. Soc. 128 (2000), 1963-1970 Request permission

Abstract:

This paper gives a precise topological description of the set of rays along which a superharmonic function on $\mathbb {R}^n$ may grow quickly. The corollary that arbitrary growth cannot occur along all rays answers a question posed by Armitage.

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