A new gap phenomenon for proper holomorphic mappings from B^n into B^N
| dc.creator | Huang, Xiaojun | |
| dc.creator | Ji, Shanyu | |
| dc.creator | Xu, Dekang | |
| dc.date | 2006-05-02 | |
| dc.date.accessioned | 2026-07-07T07:13:51Z | |
| dc.date.available | 2026-07-07T07:13:51Z | |
| dc.description | In this paper (Math. Res. Lett. 13 (2006). No 4, 509-523), the authors established a pseudo-normal form for proper holomoprhic mappings between balls in complex spaces with degenerate rank. This then was used to give a complete characterization for all proper holomorphic maps with geometric rank one, which, in particular, includes the following as an immediate application: Theorem: Any rational holomorphic map from B^n into B^N with $4\le n\le N\le 3n-4$ is equivalent to the D'Angelo map $$F_θ(z',w)=(z',(\cosθ)w,(\sinθ)z_1w, ..., (\sinθ)z_{n-1}w, (\sinθ)w^2, 0'), 0\le θ\leq π/2.$$ It is a well-known (but also quite trivial) fact that any non-constant rational CR map from a piece of the sphere $\partial {B^n}$ into the sphere $\partial {B^N}$ can be extended as a proper rational holomoprhic map from $B^n$ into $B^N$ ($N\ge n\ge 2$). By using the rationality theorem that the authors established in [HJX05], one sees that the the above theorem (and also the main theorem of the paper) holds in the same way for any non-constant $C^3$-smooth CR map from a piece of $\partial {B^n}$ into $\partial{B^N}$. The paper [Math. Res. Lett. 13 (2006). No 4, 509-523] was first electronically published by Mathematical Research Letters several months ago at its home website: http://www.mrlonline.org/mrl/0000-000-00/Huang-Ji-Xu2.pdf. (The pdf file of the printed journal version can also be downloaded at http://www.math.uh.edu/~shanyuji/rank1.pdf). | |
| dc.description | published | |
| dc.identifier | https://arxiv.org/abs/math/0605068 | |
| dc.identifier | http://arxiv.org/abs/math/0605068 | |
| dc.identifier | Math. Res. Lett. 13 (2006). No 4, 509-523 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/112632 | |
| dc.subject | Complex Variables | |
| dc.subject | Differential Geometry | |
| dc.subject | 32H | |
| dc.title | A new gap phenomenon for proper holomorphic mappings from B^n into B^N | |
| dc.type | text |