Polynomially convex embeddings of even-dimensional compact manifolds

@article{Gupta2017PolynomiallyCE,
  title={Polynomially convex embeddings of even-dimensional compact manifolds},
  author={Purvi Gupta and Rasul Shafikov},
  journal={ANNALI SCUOLA NORMALE SUPERIORE - CLASSE DI SCIENZE},
  year={2017}
}
  • Purvi GuptaR. Shafikov
  • Published 31 August 2017
  • Mathematics
  • ANNALI SCUOLA NORMALE SUPERIORE - CLASSE DI SCIENZE
We show that, for $k>1$, any $2k$-dimensional compact submanifold of $\mathbb{C}^{3k-1}$ can be perturbed to be polynomially convex and totally real except at a finite number of points. This lowers the known bound on the number of smooth functions required on every $2k$-manifold $M$ to generate a dense subalgebra of $\mathcal{C}(M)$. We also show that the obstruction to isotropic embeddability of all $2k$-dimensional manifolds in $\mathbb{C}^{3k-1}$ does not persist if we allow for K\"ahler… 
2 Citations

Polynomially convex embeddings of odd-dimensional closed manifolds

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

odd-dimensional closed

  • Mathematics
  • 2022
Given a closed orientable abstract manifold M of odd dimension 2k +1, k ≥ 2, it is natural to look for the least n such that M can be embedded in C with certain prescribed properties. We recall that

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