Bruck conjecture for solutions of first-order partial differential equations in Cm
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arXiv
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| Autores principales: | , , |
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| Formato: | Preprint |
| Publicado: |
2025
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| _version_ | 1866912847593734144 |
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| author | Majumder, Sujoy Sarkar, Nabadwip Pramanik, Debabrata |
| author_facet | Majumder, Sujoy Sarkar, Nabadwip Pramanik, Debabrata |
| contents | In this paper, we study the Brück conjecture \cite{Bruck-1996} by interpreting it through solutions of first-order partial differential equations in several complex variables. Our results show that the Brück conjecture \cite{Bruck-1996} in $\mathbb{C}^m$ holds under certain additional conditions. In pursuit of this objective, we also establish a Borel-Caratheodory theorem in $\mathbb{C}^m$ and derive several fundamental results on the order and hyper-order of entire functions in higher dimensions. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2509_02576 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Bruck conjecture for solutions of first-order partial differential equations in Cm Majumder, Sujoy Sarkar, Nabadwip Pramanik, Debabrata Complex Variables Analysis of PDEs 32A20, 32A22 and 32H30 In this paper, we study the Brück conjecture \cite{Bruck-1996} by interpreting it through solutions of first-order partial differential equations in several complex variables. Our results show that the Brück conjecture \cite{Bruck-1996} in $\mathbb{C}^m$ holds under certain additional conditions. In pursuit of this objective, we also establish a Borel-Caratheodory theorem in $\mathbb{C}^m$ and derive several fundamental results on the order and hyper-order of entire functions in higher dimensions. |
| title | Bruck conjecture for solutions of first-order partial differential equations in Cm |
| topic | Complex Variables Analysis of PDEs 32A20, 32A22 and 32H30 |
| url | https://arxiv.org/abs/2509.02576 |