Uniqueness of L1 harmonic functions on rotationally symmetric Riemannian manifolds

Minoru Murata; Tetsuo Tsuchida

doi:10.2996/kmj/1396008245

Kodai Mathematical Journal

Online ISSN : 1881-5472
Print ISSN : 0386-5991
ISSN-L : 0386-5991

Uniqueness of L¹ harmonic functions on rotationally symmetric Riemannian manifolds

Minoru Murata, Tetsuo Tsuchida

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Keywords: harmonic function, rotationally symmetric Riemannian manifold, L¹-Liouville property, nonnegative subharmonic function

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2014 Volume 37 Issue 1 Pages 1-15

DOI https://doi.org/10.2996/kmj/1396008245

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Abstract

We show that any rotationally symmetric Riemannian manifold has the L¹-Liouville property for harmonic functions, i.e., any integrable harmonic function on it must be identically constant. We also give a characterization of a manifold which carries a non-constant L¹ nonnegative subharmonic function.

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