Polynomial convexity of ∂-flat perturbations of totally real sets

Q: What type of study is this?

This is a Quantitative Study study.

Leandro Arosio; Håkan Samuelsson Kalm; Erlend Fornæss Wold

doi:10.48550/arxiv.2510.11943

October 13, 2025Open Access

Polynomial convexity of ∂-flat perturbations of totally real sets

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Key Points

The study proves polynomial convexity holds for compact sets when perturbing totally real manifolds.
Arbitrarily small perturbations are possible through diffeomorphisms maintaining closure around compact sets.
The findings use diffeomorphisms that are bar partial flat, providing a geometric tool for convexity.
This implies new methods exist for establishing polynomial convexity in complex geometrical settings.

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Implication

Analysis shows polynomial convexity can be achieved in manifolds by perturbing structures, indicating potential in geometric analysis.

Abstract

We show that if X is a totally real d-dimensional manifold attached to a polynomially convex compact set K in Cⁿ, $d<n$, then there are arbitrarily small perturbations $X'$ of X such that K∪ X' is polynomially convex. The perturbations are induced by diffeomorphisms of Cⁿ fixing K, which are ∂-flat on K∪ X, and which are arbitrarily Cᵏ-close to the identity.

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Cite This Study

Arosio et al. (2025) studied this question.

synapsesocial.com/papers/68f3793258f37cefb60d356b https://doi.org/10.48550/arxiv.2510.11943

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Polynomial convexity of ∂-flat perturbations of totally real sets

Key Points

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Implication

Abstract

Discussion

Cite This Study

Polynomial convexity of ∂-flat perturbations of totally real sets

Key Points

Ask about this paper

Implication

Abstract

Discussion

Cite This Study

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