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arXiv · 1609.09806

Liouville-type theorems on the complete gradient shrinking Ricci solitons

Huabin Ge·Shijin Zhang
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Abstract

We prove that there does not exist non-constant positive $f$-harmonic function on the complete gradient shrinking Ricci solitons. We also prove the $L^{p}(p\geq 1 \ {\rm or}\ 0<p\leq 1)$ Liouville theorems on the complete gradient shrinking Ricci solitons.

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Huabin Ge, Shijin Zhang. 2016-09-30. Liouville-type theorems on the complete gradient shrinking Ricci solitons. https://arxiv.org/abs/1609.09806

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