Please use this identifier to cite or link to this item:
http://dr.iiserpune.ac.in:8080/xmlui/handle/123456789/7518
Full metadata record
DC Field | Value | Language |
---|---|---|
dc.contributor.author | Balakumar, G. P. | en_US |
dc.contributor.author | BORAH, DIGANTA | en_US |
dc.contributor.author | Mahajan, Prachi | en_US |
dc.contributor.author | Verma, Kaushal | en_US |
dc.date.accessioned | 2022-12-16T10:27:33Z | |
dc.date.available | 2022-12-16T10:27:33Z | |
dc.date.issued | 2023-06 | en_US |
dc.identifier.citation | Annali di Matematica Pura ed Applicata (1923 -), 202(3), 1381–1410. | en_US |
dc.identifier.issn | 0373-3114 | en_US |
dc.identifier.issn | 1618-1891 | en_US |
dc.identifier.uri | https://doi.org/10.1007/s10231-022-01285-9 | en_US |
dc.identifier.uri | http://dr.iiserpune.ac.in:8080/xmlui/handle/123456789/7518 | |
dc.description.abstract | Let M be a complex manifold which admits an exhaustion by open subsets Mj each of which is biholomorphic to a fixed domain Ω⊂Cn. The main question addressed here is to describe M in terms of Ω. Building on work of Fornaess–Sibony, we study two cases, namely M is Kobayashi hyperbolic and the other being the corank one case in which the Kobayashi metric degenerates along one direction. When M is Kobayashi hyperbolic, its complete description is obtained when Ω is one of the following domains—(i) a smoothly bounded Levi corank one domain, (ii) a smoothly bounded convex domain, (iii) a strongly pseudoconvex polyhedral domain in C2, or (iv) a simply connected domain in C2 with generic piecewise smooth Levi-flat boundary. With additional hypotheses, the case when Ω is the minimal ball or the symmetrized polydisc in Cn can also be handled. When the Kobayashi metric on M has corank one and Ω is either of (i), (ii) or (iii) listed above, it is shown that M is biholomorphic to a locally trivial fibre bundle with fibre C over a holomorphic retract of Ω or that of a limiting domain associated with it. Finally, when Ω=Δ×Bn−1, the product of the unit disc Δ⊂C and the unit ball Bn−1⊂Cn−1, a complete description of holomorphic retracts is obtained. As a consequence, if M is Kobayashi hyperbolic and Ω=Δ×Bn−1, it is shown that M is biholomorphic to Ω. Further, if the Kobayashi metric on M has corank one, then M is globally a product; in fact, it is biholomorphic to Z×C, where Z⊂Ω=Δ×Bn−1 is a holomorphic retract. | en_US |
dc.language.iso | en | en_US |
dc.publisher | Springer Nature | en_US |
dc.subject | Union problem | en_US |
dc.subject | Kobayashi hyperbolic | en_US |
dc.subject | Kobayashi corank one | en_US |
dc.subject | Levi corank one domains | en_US |
dc.subject | 2023 | |
dc.title | Limits of an increasing sequence of complex manifolds | en_US |
dc.type | Article | en_US |
dc.contributor.department | Dept. of Mathematics | en_US |
dc.identifier.sourcetitle | Annali di Matematica Pura ed Applicata (1923) | en_US |
dc.publication.originofpublisher | Foreign | en_US |
Appears in Collections: | JOURNAL ARTICLES |
Files in This Item:
There are no files associated with this item.
Items in DSpace are protected by copyright, with all rights reserved, unless otherwise indicated.