Saved in:
| Main Author: | |
|---|---|
| Format: | Preprint |
| Published: |
2025
|
| Subjects: | |
| Online Access: | https://arxiv.org/abs/2507.16338 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866913952852606976 |
|---|---|
| author | Harz, Tobias |
| author_facet | Harz, Tobias |
| contents | We construct a connected, compact set $K \subset \mathbb{C}^2$ with the following property: there exist points $p \in \hat{K} \setminus K$ such that there does not exist a sequence $\{A_ν\}$ of analytic sets $A_ν\subset\subset \mathbb{C}^2$ with boundary satisfying $p \in A_ν$ for every $ν\in \mathbb{N}$ and $\lim_{ν\to\infty} bA_ν\subset K$. For every point in $\hat{K} \setminus K$, we explicitly construct a sequence of Poletsky discs, and we compute the weak limit of the pushforwards of the Green current under these discs. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2507_16338 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Approximation of polynomial hulls by analytic varieties: A counterexample Harz, Tobias Complex Variables 32E20 We construct a connected, compact set $K \subset \mathbb{C}^2$ with the following property: there exist points $p \in \hat{K} \setminus K$ such that there does not exist a sequence $\{A_ν\}$ of analytic sets $A_ν\subset\subset \mathbb{C}^2$ with boundary satisfying $p \in A_ν$ for every $ν\in \mathbb{N}$ and $\lim_{ν\to\infty} bA_ν\subset K$. For every point in $\hat{K} \setminus K$, we explicitly construct a sequence of Poletsky discs, and we compute the weak limit of the pushforwards of the Green current under these discs. |
| title | Approximation of polynomial hulls by analytic varieties: A counterexample |
| topic | Complex Variables 32E20 |
| url | https://arxiv.org/abs/2507.16338 |