Timeline for Intersection of Stein opens admits a Stein neighborhood basis?
Current License: CC BY-SA 4.0
4 events
| when toggle format | what | by | license | comment | |
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| Feb 27 at 17:38 | comment | added | Liding Yao | Once you consider an pseudoconvex open neighborhood $U=\{z:\rho(z)<0\}$ of $K$, you can certainly shrink the neighborhood, say considering $\{z:\rho(z)+\epsilon|z|^2<0\}$ for small enough $\epsilon>0$. This is going to give you a strongly pseudoconvex neighborhood. That's why I ask what convention you take for the definitions. | |
| Feb 27 at 9:18 | comment | added | Doug Liu | Dear @LidingYao, No. A connected open subset of $\mathbb{C}^n$ is Stein iff it is pseudoconvex. I guess that there is a pseudoconvex domain in $\mathbb{C}^n$ which is not strongly pseudoconvex. | |
| Feb 26 at 5:28 | comment | added | Liding Yao | For Stein neighborhood, do you specific means a strongly pseudoconvex open domain? | |
| Mar 3, 2023 at 17:21 | history | asked | Doug Liu | CC BY-SA 4.0 |