Real Analytic Sets in Complex Spaces and CR maps
| dc.creator | Shafikov, Rasul | |
| dc.date | 2006-12-28 | |
| dc.date.accessioned | 2026-07-07T07:37:29Z | |
| dc.date.available | 2026-07-07T07:37:29Z | |
| dc.description | If $R$ is a real analytic set in $\C^n$ (viewed as $\R^{2n}$), then for any point $p\in R$ there is a uniquely defined germ $X_p$ of the smallest complex analytic variety which contains $R_p$, the germ of $R$ at $p$. It is shown that if $R$ is irreducible of constant dimension, then the function $p\to\dim X_p$ is constant on a dense open subset of $R$. As an application it is proved that a continuous map from a real analytic CR manifold $M$ into $\C^N$ which is CR on some open subset of $M$ and whose graph is a real analytic set in $M\times \C^N$ is necessarily CR everywhere on $M$. | |
| dc.identifier | https://arxiv.org/abs/math/0612829 | |
| dc.identifier | http://arxiv.org/abs/math/0612829 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/120794 | |
| dc.subject | Complex Variables | |
| dc.title | Real Analytic Sets in Complex Spaces and CR maps | |
| dc.type | text |