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- W4295123616 abstract "For a H'enon map of the form $H(x, y) = (y, p(y) - ax)$, where $p$ is a polynomial of degree at least two and $a not= 0$, it is known that the sub-level sets of the Green's function $G^+_H$ associated with $H$ are Short $mathbb C^2$'s. For a given $c > 0$, we study the holomorphic automorphism group of such a Short $mathbb C^2$, namely $Omega_c = { G^+_H < c }$. The unbounded domain $Omega_c subset mathbb C^2$ is known to have smooth real analytic Levi-flat boundary. Despite the fact that $Omega_c$ admits an exhaustion by biholomorphic images of the unit ball, it turns out that its automorphism group, Aut$(Omega_c)$ 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 $mathbb C^2$'s to be biholomorphic." @default.
- W4295123616 created "2022-09-11" @default.
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- W4295123616 date "2021-08-17" @default.
- W4295123616 modified "2023-10-18" @default.
- W4295123616 title "On the automorphism group of certain Short $mathbb C^2$'s" @default.
- W4295123616 doi "https://doi.org/10.48550/arxiv.2108.07475" @default.
- W4295123616 hasPublicationYear "2021" @default.
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