A domain in $\mathbb C^4$ and its connection with $μ$-synthesis problem
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arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2026
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| _version_ | 1866908860057387008 |
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| author | Pal, Sourav Tomar, Nitin |
| author_facet | Pal, Sourav Tomar, Nitin |
| contents | We explore a domain $\mathbb F$ in $\mathbb C^4$ that has structural similarities with the hexablock $\mathbb{H} \subset \mathbb C^4$. It leads to the question if these two domains are biholomorphic. In this paper, we answer this question in negative. We provide alternative characterizations of the domain $\mathbb{F}$ and find its connection with the domains associated with $μ$-synthesis problem such as the symmetrized bidisc, the tetrablock, the pentablock and the hexablock. We also address the following question: does $\mathbb{F}$ (which is biholomorphic with $\mathbb L_4$) arise from a $μ$-synthesis problem in the same manner as $\mathbb{G}_2$ and $\mathbb{E}$ ? |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2603_01483 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | A domain in $\mathbb C^4$ and its connection with $μ$-synthesis problem Pal, Sourav Tomar, Nitin Complex Variables We explore a domain $\mathbb F$ in $\mathbb C^4$ that has structural similarities with the hexablock $\mathbb{H} \subset \mathbb C^4$. It leads to the question if these two domains are biholomorphic. In this paper, we answer this question in negative. We provide alternative characterizations of the domain $\mathbb{F}$ and find its connection with the domains associated with $μ$-synthesis problem such as the symmetrized bidisc, the tetrablock, the pentablock and the hexablock. We also address the following question: does $\mathbb{F}$ (which is biholomorphic with $\mathbb L_4$) arise from a $μ$-synthesis problem in the same manner as $\mathbb{G}_2$ and $\mathbb{E}$ ? |
| title | A domain in $\mathbb C^4$ and its connection with $μ$-synthesis problem |
| topic | Complex Variables |
| url | https://arxiv.org/abs/2603.01483 |