(From the School of Mathematics and Computer Sciences at NCU)A research paper titled “Nevanlinna theory for tropical hypersurfaces,” co-authored by Professor Cao Tingbin from NCU’s School of Mathematics and Computer Sciences and Professor Zheng Jianhua from Tsinghua University, has recently been published in Annali della Scuola Normale Superiore di Pisa-Classe di Scienze, an internationally acclaimed peer-reviewed mathematics journal. Nanchang University is listed as the first affiliation for the study.
The research marks a major breakthrough in tropical (max-plus) value distribution theory, achieving significant progress by extending the second main theorem from tropical hyperplanes to general tropical hypersurfaces for the first time. This achievement breaks a long-standing theoretical bottleneck that has confined related research to linear cases in the field for years. The research’s innovations are mainly reflected in three key aspects. First, it proposes and characterizes the concept of higher-dimensional intersection theory, laying a new foundation for related studies. Second, it improves the growth condition of functions by strengthening the tropical logarithmic derivative lemma, relaxing the requirement that hyperorder be strictly less than 1 to minimal hypertype - a modification that greatly broadens the theorem’s applicability. Third, it introduces a more concise form of the second main theorem for the one-dimensional case, enhancing the theorem’s practicality. These findings systematically refine the framework of tropical value distribution theory, establish in-depth connections with classical complex geometry, and provide a powerful theoretical tool for the research of ultradiscrete systems, tropical geometry, and related dynamical systems.
Founded in 1871, Annali della Scuola Normale Superiore di Pisa-Classe di Scienze is widely recognized as one of the world’s leading specialized journals in mathematics. Focusing on pure mathematics, theoretical physics, and other frontier fields, the journal is renowned for publishing pioneering theoretical achievements and adhering to a rigorous peer-review process. With an annual publication of approximately 60 high-quality articles, it exerts profound academic influence globally.
