Recently, the Complex Analysis research team at the Mathematics Research Institute of the School of Mathematical Sciences, Shenzhen University, has published multiple high-quality research papers in prestigious international academic journals in the field of mathematics, including Mathematische Annalen, International Mathematics Research Notices, and Nonlinearity.

01. Title: Decomposition of rational maps by stable multicurves

This work was completed by Professor Guizhen Cui and Associate Researcher Luxian Yang from the School of Mathematical Sciences, Shenzhen University, in collaboration with Professor Fei Yang from the School of Mathematics at Nanjing University. The paper was published in the renowned international journal International Mathematics Research Notices.

This research provides a combinatorial decomposition of rational functions using multicurves. It establishes a necessary and sufficient condition for the chaotic sets (Julia sets) of the subsystem dynamics within this decomposition to be disjoint. This provides a tool for studying the properties of chaotic sets in general rational functions.

https://doi.org/10.1093/imrn/rnaf147

02. Title: Generalizing Andreev's Theorem via circle patterns

This work was independently completed by Professor Ze Zhou from the School of Mathematical Sciences, Shenzhen University. The paper was published in the renowned international journal Mathematische Annalen.

Circle patterns originated from the work of German mathematician Koebe on the uniformization theorem and later played a significant role in the work of Thurston (American mathematician, Fields Medalist 1982) on the geometry and topology of 3-manifolds. Professor Zhou's paper focuses on the existence and rigidity of circle patterns with prescribed combinatorial structures and intersection angles. It generalizes the classical circle pattern theorem to allow for obtuse angles, successfully resolving a long-standing open problem in the field. The paper introduces degree theory into the study of circle patterns and creatively constructs a discrete analogue of the "weak solution/regularity theory" framework, providing new, inspiring, and practical ideas for exploring this and similar problems.

https://doi.org/10.1007/s00208-025-03286-4

03. Title: Mating Siegel and parabolic quadratic polynomials

This work was completed by Associate Researcher Yuming Fu from Shenzhen University in collaboration with Professor Fei Yang from Nanjing University. The paper was published in the prestigious international journal Nonlinearity.

This research provides the first rigorous proof that a certain class of quadratic polynomials with Siegel disks of irrational rotation can be mated with another class of quadratic polynomials with parabolic periodic points to form a global quadratic rational map. The researchers also proved that the Julia set of a class of rational maps possessing both bounded-type Siegel disks and parabolic points is locally connected, generalizing previous results. These findings deepen the understanding of the intrinsic connections between polynomial dynamical systems and rational maps, offering new insights for the classification, construction, and parameter space study of complex dynamical systems.

https://doi.org/10.1088/1361-6544/add785

The achievement of these series of results fully demonstrates the profound accumulation and strong vitality of the Shenzhen University Mathematics Research Institute at the forefront of mathematical research. The research not only projects a "Shenzhen University voice" on top international academic platforms but also showcases the original capabilities of the faculty in fundamental mathematics and interdisciplinary fields, as well as a positive trend of promoting disciplinary development through high-level collaboration. This marks the steady advancement of mathematics discipline construction at Shenzhen University to new heights, with the potential for more pioneering innovative achievements in the future.