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Polynomially convex embeddings of odd-dimensional closed manifolds

Gupta, P and Shafikov, R (2021) Polynomially convex embeddings of odd-dimensional closed manifolds. In: Journal fur die Reine und Angewandte Mathematik .

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Official URL: https://doi.org/10.1515/crelle-2021-0021


It is shown that any smooth closed orientable manifold of dimension 2k+1, k�2, admits a smooth polynomially convex embedding into C 3 k. This improves by 1 the previously known lower bound of 3� k+13k+1 on the possible ambient complex dimension for such embeddings (which is sharp when k=1. It is further shown that the embeddings produced have the property that all continuous functions on the image can be uniformly approximated by holomorphic polynomials. Lastly, the same technique is modified to construct embeddings whose images have nontrivial hulls containing no nontrivial analytic disks. The distinguishing feature of this dimensional setting is the appearance of nonisolated CR-singularities, which cannot be tackled using only local analytic methods (as done in earlier results of this kind), and a topological approach is required. © 2021 Walter de Gruyter GmbH, Berlin/Boston 2021Purvi Gupta is supported in part by a UGC CAS-II grant (Grant No. F.510/25/CAS-II/2018(SAP-I)). Rasul Shafikov is partially supported by the Natural Sciences and Engineering Research Council of Canada.

Item Type: Journal Article
Publication: Journal fur die Reine und Angewandte Mathematik
Publisher: De Gruyter Open Ltd
Additional Information: The copyright for this article belongs to the De Gruyter Open Ltd
Department/Centre: Division of Physical & Mathematical Sciences > Mathematics
Date Deposited: 16 Aug 2021 09:03
Last Modified: 16 Aug 2021 10:35
URI: http://eprints.iisc.ac.in/id/eprint/69200

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