Gupta, P and Shafikov, R (2020) Polynomially convex embeddings of even-dimensional compact manifolds. In: Annali della Scuola Normale Superiore di Pisa - Classe di Scienze, 21 . pp. 1649-1666.
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Abstract
The totally-real embeddability of any m-dimensional compact smooth manifold M into Cn, n _ b3m/2c, has several consequences: the genericity of polynomially convex embeddings of M into Cn, the existence of n smooth generators for the Banach algebra C(M), the existence of nonpolynomially convex embeddings with no analytic disks in their hulls, and the existence of special plurisubharmonic defining functions. We show that these results can be recovered even when m is even and n = b3m/2c - 1, m >2, despite the presence of complex tangencies, thus lowering the known bound for the optimal n in these (related but inequivalent) questions.
| Item Type: | Journal Article |
|---|---|
| Publication: | Annali della Scuola Normale Superiore di Pisa - Classe di Scienze |
| Publisher: | Scuola Normale Superiore |
| Additional Information: | The copyright for this article belongs to the Author(s). |
| Department/Centre: | Division of Physical & Mathematical Sciences > Mathematics |
| Date Deposited: | 23 Jan 2023 06:15 |
| Last Modified: | 23 Jan 2023 06:15 |
| URI: | https://eprints.iisc.ac.in/id/eprint/79249 |
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