Prof. Man Chun LI
Department of Mathematics
The Chinese University of Hong Kong
Biography
- Associate Professor in Department of Mathematics at The Chinese University of Hong Kong
- Research interests include Geometric Analysis, Geometric Partial Differential Equations, General Relativity
- RFS project — aims to study the existence and regularity of minimal surfaces that arise naturally in the context of geometry, phase transition and general relativity. By employing novel variational methods and non-linear partial differential equation techniques, the research aims to give a mathematically rigorous construction of minimal surfaces and analyze their singularities using modern geometric analysis tools. This project will investigate how these surfaces evolve under physical laws and their impact on related fields like phase transitions, superconductivity and numerical relativity. The findings could help in visualizing, for example, how shapes change over time and how trapped surfaces are formed in space-time according to Einstein’s equation in general relativity.
- Awards and Honours:
- RGC Senior Research Fellow (2025)
- Hong Kong Mathematical Society Young Scholar Award (2021)
- NSFC Excellent Young Scientist Fund (2020)
Project Title
- Minimal Surfaces in Geometry, Phase Transition and General Relativity
Award Citation
Professor Li Man-chun is an Associate Professor at the Department of Mathematics, The Chinese University of Hong Kong. He is a pure mathematician working in the area of differential geometry and partial differential equations. Professor Li’s research interest lies in the geometric and analytic aspects of minimal surface theory, as well as their applications in other scientific disciplines. He has received several awards and honours, such as the NSFC Excellent Young Scientist Fund and the Hong Kong Mathematical Society Young Scholar Award, in recognition of his fundamental contributions in these areas.
The proposed project under RFS studies the existence and regularity of minimal surfaces that arise in geometry, phase transition and general relativity. Novel variational methods will be employed and combined with techniques from non-linear partial differential equations to construct minimal surfaces under very general situations. It will also study the structure of singularities for such minimal surfaces using modern tools in geometric analysis and geometric measure theory.
Minimal surfaces have been extensively studied by many prominent mathematicians for over 100 years. While substantial progress has been made, there are still many remaining open questions, especially concerning their boundary behaviour. Previous work focus mostly on interior regularity theory. Boundary regularity theory, however, still remains at a relatively infant stage, but it is essential in order to reach a complete theory. This project will fill in this gap and apply the state-of-the-art techniques to study the boundary effects on minimal surfaces and their related evolution problem. Recent discoveries show that boundary effects play a vital role in general relativity and turbulence theory in the study of singularity formation. The mathematical theories developed in this project will have applications in studying the boundary effects in phase transition and superconductivity theory as well as numerical relativity.
