L²_f harmonic 1-forms on smooth metric measure spaces with positive λ₁(Δ_f)

2020/01/20 by Zhou, Jiuru
#53C20 #53C21 #Differential Geometry (math.DG) #FOS: Mathematics

paper · doi:10.48550/arxiv.2001.07037

Abstract

In this paper, we study vanishing and splitting results on a complete smooth metric measure space (Mⁿ,g,e^-fdv) with various negative m-Bakry-Émery-Ricci curvature lower bounds in terms of the first spectrum λ₁(Δ_f) of the weighted Laplacian Δ_f, i.e. Ric_m,n≥ -aλ₁(Δ_f)-b for 0

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