Instability of the Liouville property for quasi-isometric graphs and manifolds of polynomial volume growth |
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| Authors: | Itai Benjamini |
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| Institution: | (1) Hebrew University, Jerusalem, Israel |
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| Abstract: | In this note we construct two quasi-isometric graphs. One admits an infinite dimensional space of nonconstant bounded harmonic functions, while the other admits only constant bounded harmonic functions. Translation of the construction to manifolds answers a problem due to T. Lyons. |
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| Keywords: | Brownian motion harmonic function quasi-isometry |
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