Dr Min-Chun Hong's research interests are in: Non-linear Partial Differential, Equations, Geometric Analysis and Calculus of Variations.
Dr Hong received his PhD from Zhejiang University in 1988. His current research projects are in the fields of:
Journal Article: Biharmonic hypersurfaces with constant scalar curvature in space forms
Fu, Yu and Hong, Min-Chun (2018) Biharmonic hypersurfaces with constant scalar curvature in space forms. Pacific Journal of Mathematics, 294 2: 329-350. doi:10.2140/pjm.2018.294.329
Journal Article: Finite time blowup of the n-harmonic flow on n-manifolds
Cheung, Leslie Hon-Nam and Hong, Min-Chun (2017) Finite time blowup of the n-harmonic flow on n-manifolds. Calculus of Variations and Partial Differential Equations, 57 9: 1-24. doi:10.1007/s00526-017-1282-x
Journal Article: The Yang-Mills α-flow in vector bundles over four manifolds and its applications
Hong, Min-Chun, Tian, Gang and Yin, Hao (2015) The Yang-Mills α-flow in vector bundles over four manifolds and its applications. Commentarii Mathematici Helvetici, 90 1: 75-120. doi:10.4171/CMH/347
Geometric evolution problems in nonlinear partial differential equations
(2015–2017) ARC Discovery Projects
Geometric partial differential systems and their applications
(2009–2011) ARC Discovery Projects
A new enabling technology for learning and teaching quantitative skills
(2006–2008) Carrick Competitive Grants
Existence of solutions of the Ericksen Leslie system on Riemann surfaces and its application
Doctor Philosophy
Mathematical modelling of fluid flow models
(2016) Doctor Philosophy
Finite time blow up of the n harmonic flow on n manifolds
Doctor Philosophy
Some analytic aspects of liquid crystal configurations
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.
Biharmonic hypersurfaces with constant scalar curvature in space forms
Fu, Yu and Hong, Min-Chun (2018) Biharmonic hypersurfaces with constant scalar curvature in space forms. Pacific Journal of Mathematics, 294 2: 329-350. doi:10.2140/pjm.2018.294.329
Finite time blowup of the n-harmonic flow on n-manifolds
Cheung, Leslie Hon-Nam and Hong, Min-Chun (2017) Finite time blowup of the n-harmonic flow on n-manifolds. Calculus of Variations and Partial Differential Equations, 57 9: 1-24. doi:10.1007/s00526-017-1282-x
The Yang-Mills α-flow in vector bundles over four manifolds and its applications
Hong, Min-Chun, Tian, Gang and Yin, Hao (2015) The Yang-Mills α-flow in vector bundles over four manifolds and its applications. Commentarii Mathematici Helvetici, 90 1: 75-120. doi:10.4171/CMH/347
Blow-up criteria of strong solutions to the Ericksen-Leslie system in ℝ3
Hong, Min-Chun, Li, Jinkai and Xin, Zhouping (2014) Blow-up criteria of strong solutions to the Ericksen-Leslie system in ℝ3. Communications in Partial Differential Equations, 39 7: 1284-1328. doi:10.1080/03605302.2013.871026
Hong, Min-Chun (2014) Some results on harmonic maps. Bulletin of the Institute of Mathematics Academia Sinica New Series, 9 2: 187-221.
On the sacks-uhlenbeck flow of Riemannian surfaces
Hong, Min-Chun and Yin, Hao (2013) On the sacks-uhlenbeck flow of Riemannian surfaces. Communications in Analysis and Geometry, 21 5: 917-955. doi:10.4310/CAG.2013.v21.n5.a3
Global existence of solutions of the liquid crystal flow for the Oseen–Frank model in R2
Hong, Min-Chun and Xin, Zhouping (2012) Global existence of solutions of the liquid crystal flow for the Oseen–Frank model in R2. Advances in Mathematics, 231 3-4: 1364-1400. doi:10.1016/j.aim.2012.06.009
Partial regularity of a minimizer of the relaxed energy for biharmonic maps
Hong, Min-Chun and Yin, Hao (2012) Partial regularity of a minimizer of the relaxed energy for biharmonic maps. Journal of Functional Analysis, 262 2: 682-718. doi:10.1016/j.jfa.2011.10.003
A new approximation of relaxed energies for harmonic maps and the Faddeev model
Giaquinta, Mariano, Hong, Min-Chun and Yin, Hao (2011) A new approximation of relaxed energies for harmonic maps and the Faddeev model. Calculus of Variations and Partial Differential Equations, 41 1-2: 45-69. doi:10.1007/s00526-010-0353-z
Global existence of solutions of the simplified Ericksen-Leslie system in dimension two
Hong, Min-Chun (2011) Global existence of solutions of the simplified Ericksen-Leslie system in dimension two. Calculus of Variations And Partial Differential Equations, 40 1-2: 15-36. doi:10.1007/s00526-010-0331-5
Global existence for the Seiberg–Witten flow
Hong, Min-Chun and Schabrun, Lorenz (2010) Global existence for the Seiberg–Witten flow. Communications In Analysis And Geometry, 18 3: 433-473.
Curvature flow to the Nirenberg problem
Ma, Li and Hong, Min-Chun (2010) Curvature flow to the Nirenberg problem. Archiv der Mathematik, 94 3: 277-289. doi:10.1007/s00013-010-0101-9
The heat flow for H-systems on higher dimensional manifolds
Hong, Min-Chun and Hsu, Deliang (2010) The heat flow for H-systems on higher dimensional manifolds. Indiana University Mathematics Journal, 59 3: 761-790.
Anti-self-dual connections and their related flow on 4-manifolds
Hong, M.-C. and Yu, Z. (2008) Anti-self-dual connections and their related flow on 4-manifolds. Calculus of Variations, 31 3: 325-349. doi:10.1007/s00526-007-0114-9
Partial regularity of weak solutions to Maxwell's equations in a quasi-static electromagnetic field
Hong, M.-C., Tonegawa, Y. and Alzubaidi, Y. (2008) Partial regularity of weak solutions to Maxwell's equations in a quasi-static electromagnetic field. Methods and Applications of Analysis, 15 2: 199-215.
Stability of the equator map for the hessian energy
Hong, M. C. and Thompson, B. (2007) Stability of the equator map for the hessian energy. Proceedings of the American Mathematical Society, 135 10: 3163-3170. doi:10.1090/S0002-9939-07-08950-2
Hong, M. C. (2007) Existence of infinitely many equilibrium configurations of a liquid crystal system prescribing the same nonconstant boundary value. Pacific Journal of Mathematics, 232 1: 177-206. doi:10.2140/pjm.2007.232.177
Partial regularity of stable p-harmonic maps into spheres
Hong, M. C. (2007) Partial regularity of stable p-harmonic maps into spheres. The Bulletin of the Australian Mathematical Society, 76 2: 297-305.
Regularity and relaxed problems of minimizing biharmonic maps into spheres
Hong, Min-Chun and Wang, Changyou (2005) Regularity and relaxed problems of minimizing biharmonic maps into spheres. Calculus of Variations and Partial Differential Equations, 23 4: 425-450. doi:10.1007/s00526-004-0309-2
Asymptotical behaviour of the Yang-Mills flow and singular Yang-Mills connections
Hong, Min-Chun and Tian, Gang (2004) Asymptotical behaviour of the Yang-Mills flow and singular Yang-Mills connections. Mathematische Annalen, 330 3: 441-472. doi:10.1007/s00208-004-0539-9
Global existence of the m-equivariant Yang-Mills flow in four dimensional spaces
Hong, Min-Chun and Tian, Gang (2004) Global existence of the m-equivariant Yang-Mills flow in four dimensional spaces. Communications In Analysis And Geometry, 12 1: 183-211.
Partial regularity of minimizers of a functional involving forms and maps
Giaquinta, M and Hong, MC (2004) Partial regularity of minimizers of a functional involving forms and maps. Nodea-nonlinear Differential Equations And Applications, 11 4: 469-490. doi:10.1007/s00030-0004-2015-3
Partial regularity of weak solutions of the liquid crystal equilibrium system
Hong, Min-Chun (2004) Partial regularity of weak solutions of the liquid crystal equilibrium system. Indiana University Mathematics Journal, 53 5: 1401-1414. doi:10.1512/iumj.2004.53.2459
Minimizing harmonic maps into ellipsoids and harmonic diffeomorphisms
Hong, MC (2002) Minimizing harmonic maps into ellipsoids and harmonic diffeomorphisms. Mathematische Zeitschrift, 241 2: 313-327. doi:10.1007/s002090200416
Heat flow for Yang-Mills-Higgs fields, part II
Yi,Fang and Hong, MC (2001) Heat flow for Yang-Mills-Higgs fields, part II. Chinese Annals of Mathematics Series B, 22 2: 211-222. doi:10.1142/S0252959901000206
Heat flow for the Yang-Mills-Higgs field and the Hermitian Yang-Mills-Higgs metric
Hong, MC (2001) Heat flow for the Yang-Mills-Higgs field and the Hermitian Yang-Mills-Higgs metric. Annals of Global Analysis And Geometry, 20 1: 23-46. doi:10.1023/A:1010688223177
On the minimality of the p-harmonic map - x/vertical bar x vertical bar : B-n -> Sn-1
Hong, MC (2001) On the minimality of the p-harmonic map - x/vertical bar x vertical bar : B-n -> Sn-1. Calculus of Variations And Partial Differential Equations, 13 4: 459-468.
Heat flow for Yang-Mills-Higgs fields, part I
Yi, Fang and Hong, MC (2000) Heat flow for Yang-Mills-Higgs fields, part I. Chinese Annals of Mathematics Series B, 21 4: 453-472. doi:10.1142/S0252959900000455
On the Jager-Kaul theorem concerning harmonic maps
Hong, MC (2000) On the Jager-Kaul theorem concerning harmonic maps. Annales De L Institut Henri Poincare-analyse Non Lineaire, 17 1: 35-46. doi:10.1016/S0294-1449(99)00103-1
On the hausdorff dimension of the singular set of stable-stationary harmonic maps
Hong, MC (1999) On the hausdorff dimension of the singular set of stable-stationary harmonic maps. Communications In Partial Differential Equations, 24 11-12: 1967-1985. doi:10.1080/03605309908821490
On the singular set of stable-stationary harmonic maps
Hong, MC and Wang, CY (1999) On the singular set of stable-stationary harmonic maps. Calculus of Variations And Partial Differential Equations, 9 2: 141-156. doi:10.1007/s005260050135
Some new examples for nonuniqueness of the evolution problem of harmonic maps
Hong, MC (1998) Some new examples for nonuniqueness of the evolution problem of harmonic maps. Communications In Analysis And Geometry, 6 4: 809-818. doi:10.4310/CAG.1998.v6.n4.a7
Asymptotic limits of a self-dual Ginzburg-Landau functional in bounded domains
Hong, MC (1998) Asymptotic limits of a self-dual Ginzburg-Landau functional in bounded domains. Manuscripta Mathematica, 97 2: 251-267. doi:10.1007/s002290050100
Two estimates concerning asymptotics of the minimizations of a Ginzburg-Landau functional
Hong, MC (1997) Two estimates concerning asymptotics of the minimizations of a Ginzburg-Landau functional. Journal of The Australian Mathematical Society Series A-pure Mathematics And Statistics, 62 128-140.
Hong M.-C. (1996) Asymptotic behavior for minimizers of a Ginzburg-Landau-type functional in higher dimensions associated with n-harmonic maps. Advances in Differential Equations, 1 4: 611-634.
Multiple Solutions of the Static Landau-Lifshitz Equation From B-2 Into S-2
Hong, MC and Lemaire, L (1995) Multiple Solutions of the Static Landau-Lifshitz Equation From B-2 Into S-2. Mathematische Zeitschrift, 220 2: 295-306. doi:10.1007/BF02572616
Hong, MC (1995) The Landau-Lifshitz Equation with the External-Field - a New Extension for Harmonic Maps with Values in S-2. Mathematische Zeitschrift, 220 2: 171-188. doi:10.1007/BF02572608
On a Problem of Bethuel, Brezis and Helein Concerning the Ginzburg-Landau Functional
Hong, MC (1995) On a Problem of Bethuel, Brezis and Helein Concerning the Ginzburg-Landau Functional. Comptes Rendus De L Academie Des Sciences Serie I-Mathematique, 320 6: 679-684.
Heat-Flow of P-Harmonic Maps with Values Into Spheres
Chen, YM, Hong, MC and Hungerbuhler, N (1994) Heat-Flow of P-Harmonic Maps with Values Into Spheres. Mathematische Zeitschrift, 215 1: 25-35. doi:10.1007/BF02571698
The Landau-Lifshitz Equation of the Ferromagnetic Spin Chain and Harmonic Maps
Guo, BL and Hong, MC (1993) The Landau-Lifshitz Equation of the Ferromagnetic Spin Chain and Harmonic Maps. Calculus of Variations and Partial Differential Equations, 1 3: 311-334. doi:10.1007/BF01191298
Liouville Theorems for Exponentially Harmonic-Functions On Riemannian-Manifolds
Hong, MC (1992) Liouville Theorems for Exponentially Harmonic-Functions On Riemannian-Manifolds. Manuscripta Mathematica, 77 1: 41-46.
On the Conformal Equivalence of Harmonic Maps and Exponentially Harmonic Maps
Hong, MC (1992) On the Conformal Equivalence of Harmonic Maps and Exponentially Harmonic Maps. Bulletin of the London Mathematical Society, 24 488-492.
The Equator Map and the Negative Exponential Functional
Hong, MC (1992) The Equator Map and the Negative Exponential Functional. Manuscripta Mathematica, 75 1: 49-63. doi:10.1007/BF02567071
Some Remarks On the Minimizers of Variational Integrals with Nonstandard Growth-Conditions
Hong, MC (1992) Some Remarks On the Minimizers of Variational Integrals with Nonstandard Growth-Conditions. Bollettino Della Unione Matematica Italiana, 6A 1: 91-101.
Partial Regularities of Minimizers of Certain Quadratic Functionals with Unbounded Obstacles
Hong, MC (1992) Partial Regularities of Minimizers of Certain Quadratic Functionals with Unbounded Obstacles. Annali Di Matematica Pura Ed Applicata, 161 113-138.
Existence and Partial Regularity in the Calculus of Variations
Hong, MC (1987) Existence and Partial Regularity in the Calculus of Variations. Annali Di Matematica Pura Ed Applicata, 149 311-328.
Geometric evolution problems in nonlinear partial differential equations
(2015–2017) ARC Discovery Projects
Geometric partial differential systems and their applications
(2009–2011) ARC Discovery Projects
A new enabling technology for learning and teaching quantitative skills
(2006–2008) Carrick Competitive Grants
Variational methods in partial differential equations
(2006–2008) ARC Linkage International
Geometric variational problems and nonlinear partial differential systems
(2004–2006) ARC Discovery Projects
Existence of solutions of the Ericksen Leslie system on Riemann surfaces and its application
Doctor Philosophy — Principal Advisor
Finite time blow up of the n harmonic flow on n manifolds
Doctor Philosophy — Principal Advisor
Other advisors:
Mathematical modelling of fluid flow models
(2016) Doctor Philosophy — Principal Advisor
(2011) Doctor Philosophy — Principal Advisor
Other advisors:
(2010) Doctor Philosophy — Principal Advisor
Other advisors: