Sharp Dimension Estimates of Holomorphic Functions and Rigidity
| dc.creator | Chen, Bing-Long | |
| dc.creator | Fu, Xiao-Yong | |
| dc.creator | Yin, Le | |
| dc.creator | Zhu, Xi-Ping | |
| dc.date | 2003-11-11 | |
| dc.date.accessioned | 2026-07-07T05:02:47Z | |
| dc.date.available | 2026-07-07T05:02:47Z | |
| dc.description | Let $M^n$ be a complete noncompact K$\ddot{a}$hler manifold of complex dimension $n$ with nonnegative holomorphic bisectional curvature. Denote by $\mathcal{O}$$_d(M^n)$ the space of holomorphic functions of polynomial growth of degree at most $d$ on $M^n$. In this paper we prove that $$dim_{\mathbb{C}}{\mathcal{O}}_d(M^n)\leq dim_{\mathbb{C}}{\mathcal{O}}_{[d]}(\mathbb{C}^n),$$ for all $d>0$, with equality for some positive integer $d$ if and only if $M^n$ is holomorphically isometric to $\mathbb{C}^n$. We also obtain sharp improved dimension estimates when its volume growth is not maximal or its Ricci curvature is positive somewhere. | |
| dc.description | 24 pages | |
| dc.identifier | https://arxiv.org/abs/math/0311164 | |
| dc.identifier | http://arxiv.org/abs/math/0311164 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/69148 | |
| dc.subject | Differential Geometry | |
| dc.subject | Complex Variables | |
| dc.title | Sharp Dimension Estimates of Holomorphic Functions and Rigidity | |
| dc.type | text |