The modified Calabi-Yau problems for CR-manifolds and applications
| dc.creator | Cao, JIanguo | |
| dc.creator | Chang, Shu-Cheng | |
| dc.date | 2008-01-22 | |
| dc.date | 2008-04-22 | |
| dc.date.accessioned | 2026-07-07T09:33:37Z | |
| dc.date.available | 2026-07-07T09:33:37Z | |
| dc.description | In this paper, we derive a partial result related to a question of Yau: "Does a simply-connected complete Kähler manifold M with negative sectional curvature admit a bounded non-constant holomorphic function?" Main Theorem. Let $M^{2n}$ be a simply-connected complete Kähler manifold M with negative sectional curvature $ \le -1 $ and $S_\infty(M)$ be the sphere at infinity of $M$. Then there is an explicit {\it bounded} contact form $β$ defined on the entire manifold $M^{2n}$. Consequently, the sphere $S_\infty(M)$ at infinity of M admits a {\it bounded} contact structure and a bounded pseudo-Hermitian metric in the sense of Tanaka-Webster. We also discuss several open modified problems of Calabi and Yau for Alexandrov spaces and CR-manifolds. | |
| dc.description | The new version is more accurate on citing other people's work | |
| dc.identifier | https://arxiv.org/abs/0801.3431 | |
| dc.identifier | http://arxiv.org/abs/0801.3431 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/159196 | |
| dc.subject | Differential Geometry | |
| dc.subject | Complex Variables | |
| dc.subject | 53C20, 53C23 | |
| dc.title | The modified Calabi-Yau problems for CR-manifolds and applications | |
| dc.type | text |