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arXiv · 2509.02576

Bruck conjecture for solutions of first-order partial differential equations in Cm

Sujoy Majumder·Nabadwip Sarkar·Debabrata Pramanik
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Abstract

In this paper, we study the Br\"{u}ck conjecture \cite{Bruck-1996} by interpreting it through solutions of first-order partial differential equations in several complex variables. Our results show that the Br\"{u}ck 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.

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Sujoy Majumder, Nabadwip Sarkar, Debabrata Pramanik. 2025-08-25. Bruck conjecture for solutions of first-order partial differential equations in Cm. https://arxiv.org/abs/2509.02576

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