Liouville theorem for bounded harmonic functions on manifolds and graphs satisfying non-negative curvature dimension condition

Bobo Hua

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arXiv · 1702.00961

Liouville theorem for bounded harmonic functions on manifolds and graphs satisfying non-negative curvature dimension condition

Bobo Hua

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Abstract

Brighton [Bri13] proved the Liouville theorem for bounded harmonic functions on weighted manifolds satisfying non-negative curvature dimension condition, i.e. $CD(0,\infty).$ In this paper, we provide a new proof of this result by using the reverse Poincaré inequality. Moreover, we adopt this approach to prove the Liouville theorem for bounded harmonic functions on graphs satisfying the $CD(0,\infty)$ condition.

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Bobo Hua. 2018-06-14. Liouville theorem for bounded harmonic functions on manifolds and graphs satisfying non-negative curvature dimension condition. https://arxiv.org/abs/1702.00961

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