2024/01/05 by Fei He, He, Fei, Jianyu Ou +1
Mathematics · #Complex Variables (math.CV) #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometry and complex manifolds #Holomorphic and Operator Theory
paper · pdf · doi:10.48550/arxiv.2401.02685
openalex publication_date 2024/01/05 · openalex created_date 2024/01/13 · openalex updated_date 2026/07/28
We study polynomial growth holomorphic functions and forms on complete gradient shrinking Ricci solitons. By relating to the spectral data of the f-Laplacian, we show that the dimension of the space of polynomial growth holomorphic functions or holomorphic (p,0)-forms are finite. In particular, a sharp dimension estimate for the space of linear growth holomorphic functions was obtained. Under some additional curvature assumption, we prove an almost sharp estimate for the frequency of polynomial growth holomorphic functions, which was used to obtain dimension upper bound as a power function of the polynomial order.