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arXiv · 2510.11943

Polynomial convexity of $\bar\partial$-flat perturbations of totally real sets

Leandro Arosio·Håkan Samuelsson Kalm·Erlend F. Wold
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Abstract

We show that if $X$ is a totally real $d$-dimensional manifold attached to a polynomially convex compact set $K$ in $\mathbb{C}^n$, $d<n$, then there are arbitrarily small perturbations $X'$ of $X$ such that $K\cup X'$ is polynomially convex. The perturbations are induced by diffeomorphisms of $\mathbb{C}^n$ fixing $K$, which are $\bar\partial$-flat on $K\cup X$, and which are arbitrarily $C^k$-close to the identity.

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Leandro Arosio, Håkan Samuelsson Kalm, Erlend F. Wold. 2025-10-13. Polynomial convexity of $\bar\partial$-flat perturbations of totally real sets. https://arxiv.org/abs/2510.11943

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