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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2025
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2503.19765 |
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Table of Contents:
- We show that any compact smooth real $n$-dimensional manifold $M$ with $n\leq 11$ can be smoothly embedded into $\mathbb{C}^{n+1}$ as a polynomially convex set. In general, there is no such embedding into $\mathbb{C}^n$. This solves a problem by Izzo and Stout for $n\leq 11$. Additionally, we show that the image $\widetilde{M}$ of $M$ in $\mathbb{C}^{n+1}$ is stratified totally real. As a consequence, by a result in [13], each continuous complex-valued functions on $\widetilde{M}$ is the uniform limit on $\widetilde{M}$ of holomorphic polynomials in $\mathbb{C}^{n+1}$. Our proof is based on the jet transversality theorem and a slight improvement of a perturbation result by the first and the third author.