Sharp Dimension Estimates of Holomorphic Functions and Rigidity
Chen, Bing-Long · Fu, Xiao-Yong · Yin, Le · Zhu, Xi-Ping
Original · EN
Let Mⁿ be a complete noncompact Kahler manifold of complex dimension n with nonnegative holomorphic bisectional curvature. Denote by Od(Mⁿ) the space of holomorphic functions of polynomial growth of degree at most d on Mⁿ. In this paper we prove that dimCOd(Mⁿ)≤ dimCO[d](Cⁿ), for all d>0, with equality for some positive integer d if and only if Mⁿ is holomorphically isometric to Cⁿ. We also obtain sharp improved dimension estimates when its volume growth is not maximal or its Ricci curvature is positive somewhere.
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