On the localization principle for the automorphisms of pseudoellipsoids

dc.creatorLanducci, Mario
dc.creatorSpiro, Andrea
dc.date2008-11-24
dc.date.accessioned2026-07-07T10:20:40Z
dc.date.available2026-07-07T10:20:40Z
dc.descriptionWe 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.description7 pages; to appear on Proceedings of AMS
dc.identifierhttps://arxiv.org/abs/0811.3861
dc.identifierhttp://arxiv.org/abs/0811.3861
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/174925
dc.subjectComplex Variables
dc.subject32H12, 32H02, 32H35
dc.titleOn the localization principle for the automorphisms of pseudoellipsoids
dc.typetext

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