On the localization principle for the automorphisms of pseudoellipsoids
| dc.creator | Landucci, Mario | |
| dc.creator | Spiro, Andrea | |
| dc.date | 2008-11-24 | |
| dc.date.accessioned | 2026-07-07T10:20:40Z | |
| dc.date.available | 2026-07-07T10:20:40Z | |
| dc.description | We show that Alexander's extendibility theorem for a local automorphism of the unit ball is valid also for a local automorphism $f$ of a pseudoellipsoid $\E^n_{(p_1, ..., p_{k})} \= \{z \in \C^n : \sum_{j= 1}^{n - k}|z_j|^2 + |z_{n-k+1}|^{2 p_1} + ... + |z_n|^{2 p_{k}} < 1 \}$, provided that $f$ is defined on a region $\U \subset \E^n_{(p)}$ such that: i) $\partial \U \cap \partial \E^n_{(p)}$ contains an open set of strongly pseudoconvex points; ii) $\U \cap \{z_i = 0 \} \neq \emptyset$ for any $n-k +1 \leq i \leq n$. By the counterexamples we exhibit, such hypotheses can be considered as optimal. | |
| dc.description | 7 pages; to appear on Proceedings of AMS | |
| dc.identifier | https://arxiv.org/abs/0811.3861 | |
| dc.identifier | http://arxiv.org/abs/0811.3861 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/174925 | |
| dc.subject | Complex Variables | |
| dc.subject | 32H12, 32H02, 32H35 | |
| dc.title | On the localization principle for the automorphisms of pseudoellipsoids | |
| dc.type | text |