# Polynomially convex embeddings of odd-dimensional closed manifolds

@article{Gupta2020PolynomiallyCE,
title={Polynomially convex embeddings of odd-dimensional closed manifolds},
author={Purvi Gupta and Rasul Shafikov},
journal={Journal f{\"u}r die reine und angewandte Mathematik (Crelles Journal)},
year={2020},
volume={2021},
pages={273 - 299}
}
• Published 26 September 2020
• Mathematics
• Journal für die reine und angewandte Mathematik (Crelles Journal)
Abstract It is shown that any smooth closed orientable manifold of dimension 2⁢k+1{2k+1}, k≥2{k\geq 2}, admits a smooth polynomially convex embedding into ℂ3⁢k{\mathbb{C}^{3k}}. This improves by 1 the previously known lower bound of 3⁢k+1{3k+1} on the possible ambient complex dimension for such embeddings (which is sharp when k=1{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…

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