Timeline for Kähler manifold with a global potential
Current License: CC BY-SA 4.0
6 events
| when toggle format | what | by | license | comment | |
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| Jul 3, 2018 at 8:29 | comment | added | user94640 | I want to prove some vanising results by the method of Donnelly-Fefferman Ann.Math.118(1983). But $\bar{\partial}f$ and $\partial{f}$ in the process of calculation are always appearing. In my question, I only suppose $f$ has a bounded. I has no way to bounded $\bar{\partial}f$ and $\partial{f}$ by $f$. | |
| Jul 3, 2018 at 8:20 | comment | added | user94640 | In my question, I suppose that $f$ is bounded and $\omega$ is induced by a complete metric. | |
| Jul 2, 2018 at 22:28 | comment | added | user48958 | If $\omega$ is not complete, then it is trivial to show that the vanishing you mentioned does not hold. Take $X$ to be the unit ball in ${\mathbb C}^n$ and $f=\vert z\vert^2$. Then $H^{0,0}_{(2)}(X)$ is infinite dimensional. | |
| Jul 2, 2018 at 22:18 | comment | added | user48958 | Let me make sure I understand your question. Is your $f$ such that $f$ is bounded AND $\omega=i\partial\bar\partial f$ is induced by a complete metric, or $f$ is just bounded, and $\omega$ is not necessarily complete? | |
| Jul 1, 2018 at 14:18 | history | edited | Arun Debray | CC BY-SA 4.0 |
\"{a} -> ä
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| Jul 1, 2018 at 13:57 | history | asked | user94640 | CC BY-SA 4.0 |