Polynomially Convex Embeddings of Even-Dimensional Compact Manifolds

2017/08/31 by Gupta, Purvi, Shafikov, Rasul · 2 citations
#32E20 #32V40 #53D12 #Complex Variables (math.CV) #FOS: Mathematics

paper · doi:10.48550/arxiv.1709.00059

Abstract

The totally-real embeddability of any 2k-dimensional compact manifold M into \mathbb Cⁿ, n≥ 3k, has several consequences: the genericity of polynomially convex embeddings of M into \mathbb Cⁿ, the existence of n smooth generators for the Banach algebra \mathcal C(M), the existence of nonpolynomially convex embeddings with no analytic disks in their hulls, and the existence of special plurisubharmonic defining functions. We show that these results can be recovered even when n=3k-1, k>1, despite the presence of complex tangencies, thus lowering the known bound for the optimal n in these (related but inequivalent) questions.

Cited by

• Local Polynomial Convexity at Hyperbolic CR-singularities in M ⊂ ℂⁿ
• Polynomial convexity of ∂-flat perturbations of totally real sets

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