On Lᵖ-Liouville property for smooth metric measure spaces

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In this short paper we study Lfᵖ-Liouville property with 0<p<1 for nonnegative f-subharmonic functions on a complete noncompact smooth metric measure space (M,g,e⁻ᶠdv) with Ricfᵐ bounded below for 0<m≤∞. We prove a sharp Lfᵖ-Liouville theorem when 0<m<∞. We also prove an Lfᵖ-Liouville theorem when Ricf≥ 0 and |f(x)|≤ δ(n) r(x).