# 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} }

Abstract It is shown that any smooth closed orientable manifold of dimension 2k+1{2k+1}, k≥2{k\geq 2}, admits a smooth polynomially convex embedding into ℂ3k{\mathbb{C}^{3k}}. This improves by 1 the previously known lower bound of 3k+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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