Liouville property for f-harmonic functions with polynomial growth
classification
🧮 math.DG
math.AP
keywords
growthharmonicliouvillepolynomialpropertybakry-completecurvature
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We prove a Liouville property for any $f$-harmonic function with polynomial growth on a complete noncompact smooth metric measure space $(M,g,e^{-f}dv)$ when the Bakry-\'Emery Ricci curvature is nonnegative and its diameter of geodesic sphere has sublinear growth.
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