On convex to pseudoconvex mappings
| dc.creator | Ivashkovich, S. | |
| dc.date | 2009-03-10 | |
| dc.date.accessioned | 2026-07-07T12:50:55Z | |
| dc.date.available | 2026-07-07T12:50:55Z | |
| dc.description | In the works of Darboux and Walsh it was remarked that a one to one self mapping of $\rr^3$ which sends convex sets to convex ones is affine. It can be remarked also that a $\calc^2$-diffeomorphism $F:U\to U^{'}$ between two domains in $\cc^n$, $n\ge 2$, which sends pseudoconvex hypersurfaces to pseudoconvex ones is either holomorphic or antiholomorphic. \smallskip In this note we are interested in the self mappings of $\cc^n$ which send convex hypersurfaces to pseudoconvex ones. Their characterization is the following: {\it A $\calc^2$ - diffeomorphism $F:U'\to U$ (where $U', U\subset \cc^n$ are domains) sends convex hypersurfaces to pseudoconvex ones if and only if the inverse map $Φ\deff F^{-1}$ is weakly pluriharmonic, i.e. it satisfies some nice second order PDE very close to $\d\bar\d Φ= 0$.} In fact all pluriharmonic $Φ$-s do satisfy this equation, but there are also other solutions. | |
| dc.identifier | https://arxiv.org/abs/0903.1787 | |
| dc.identifier | http://arxiv.org/abs/0903.1787 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/222831 | |
| dc.subject | Complex Variables | |
| dc.subject | Metric Geometry | |
| dc.subject | 32F10 | |
| dc.title | On convex to pseudoconvex mappings | |
| dc.type | text |