Associate Professor Min-Chun Hong

Associate Professor

Mathematics
Faculty of Science
hong@maths.uq.edu.au
+61 7 334 69036

Overview

Dr Min-Chun Hong has solved a number of open problems and conjectures on harmonic maps, liquid crystals and Yang Mills equations in the areas of nonlinear partial differential equations and geometric analysis. He has collaborated with top mathematicians such as Professor Mariano Giaquinta (SNS-Pisa), Professor Jurgen Jost (Germany), Professor Michael Struwe (Zurich), Professor Gang Tian (Princeton) and Professor Zhouping Xin (Hong Kong).

Some highlights of his research after joining UQ in 2004 are:

In the area of harmonic maps, collaborated with Giaquinta and Yin (Calc. Var. PDEs 2011), he developed a new approximation of the Dirichlet energy, yielding a new proof on partial regularity of minimizers of the relax energy for harmonic maps as well as for the Faddeev model. The method leads to solve an open problem on partial regularity in the relax energy of biharmonic maps by him and Hao Yin (J. Funct. Anal. 2012).

Based on the well-known result of Sack and Uhlenbeck in 1981 (Uhlenbeck 2019 Abel Award Winner), with collaboration of Hao Yin in 2013, he introduced the Sack-Uhlenbeck flow to prove new existence results of the harmonic map flow in 2D and made new application to homotopy classes. More recently, collaborated with his PhD student L. Cheng (Calc. Var. PDEs 2018), he settled a conjecture of Hungerbuhler on the n-harmonic map flow.

In the area of Yang-Mills equations, with Gang Tian (Math. Ann. 2004), he established asymptotic behaviour of the Yang-Mills flow to prove the existence of singular Hermitian-Yang-Mills connections, which was used to settle a well-known conjecture of Bando and Siu. Collaborated with Tian and Yin (Commun. Math. Helv. 2015), he extended the Sack-Uhlenbeck program to Yang-Mills equations and introduced the Yang-Mills alpha-flow to approximate the Yang-Mills flow in 4D. More recently, collaborated with his PhD student L. Schabrun (Calc. Var. PDEs 2019), we proved the energy identity for a sequence of Yang-Mills α-connections.

In the area of liquid crystals, he (Calc. Var. PDEs 2011) resolved a long-standing open problem on the global existence of the simplified Ericksen-Leslie system in 2D (a highly cited paper in Web of Science). Collaborated with Zhouping Xin (Adv. Math. 2012), he solved the global existence problem on the Ericksen-Leslie system with unequal Frank constants in 2D. Collaborated with Li and Xin (CPDE 2014), he resolved a problem on converging of the approximate Ericksen-Leslie system in 3D.

Qualifications

  • Master of Science, Nankai
  • Bachelor of Science, Nankai
  • PhD in Mathematics, Zhejiang

Publications

View all Publications

Supervision

  • Doctor Philosophy

  • Doctor Philosophy

  • (2016) Doctor Philosophy

View all Supervision

Publications

Book Chapter

  • Hong, Min-Chun (2010). Some analytic aspects of liquid crystal configurations. In Baojun Bian, Shenghong Li and Xu-Jia Wang (Ed.), Trends in partial differential equations (pp. 193-211) Beijing-Boston: Higher Education Press and International Press.

  • Hong, Min-Chun , Jost, Jurgen and Struwe, Michael (1996). Asymptotic limits of a Ginzburg-Landau type functional. In Jürgen Jost (Ed.), Geometric analysis and the calculus of variations (pp. 99-124) Boston, MA, United States: International Press.

Journal Article

Grants (Administered at UQ)

PhD and MPhil Supervision

Current Supervision

  • Doctor Philosophy — Principal Advisor

  • Doctor Philosophy — Principal Advisor

    Other advisors:

Completed Supervision