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On the Automorphism Group of Certain Short C2s

Bera, S and Pal, R and Verma, K (2023) On the Automorphism Group of Certain Short C2s. In: International Mathematics Research Notices, 2023 (17). pp. 14515-14546.

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Official URL: https://doi.org/10.1093/imrn/rnac235


For a Henon map of the form, where is a polynomial of degree at least two and, it is known that the sub-level sets of the Green's function associated with are Short 's. For a given 0, we study the holomorphic automorphism group of such a Short, namely Ωc = G+H. The unbounded domain is known to have smooth real analytic Levi-flat boundary. Despite the fact that admits an exhaustion by biholomorphic images of the unit ball, it turns out that its automorphism group,, cannot be too large. On the other hand, examples are provided to show that these automorphism groups are non-trivial in general. We also obtain necessary and sufficient conditions for such a pair of Short 's to be biholomorphic. © 2022 The Author(s). Published by Oxford University Press. All rights reserved.

Item Type: Journal Article
Publication: International Mathematics Research Notices
Publisher: Oxford University Press
Additional Information: The copyright for this article belongs to the Oxford University Press.
Department/Centre: Division of Physical & Mathematical Sciences > Mathematics
Date Deposited: 17 Dec 2023 09:11
Last Modified: 17 Dec 2023 09:11
URI: https://eprints.iisc.ac.in/id/eprint/83450

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