Publications and Preprints

  1. LEUNG, Man Chun: Pinching theorem on asymptotically hyperbolic spaces, International Journal of Mathematics 4, 831-857 (1993).
  2. LEUNG, Man Chun: Conformal scalar curvature equations on complete manifolds, Commun. in Partial Differential Equations 20, 367-417 (1995).
  3. LEUNG, Man Chun: Asymptotic behavior of rotationally symmetric p-harmonic maps, Applicable Analysis 61, 1-15 (1996).
  4. LEUNG, Man Chun: On the L^{n/2}-norm of scalar curvature, Illinois J. Math. 40, 606--631 (1996).
  5. LEUNG, Man Chun: Lower bounds on some geometric quantities and applications, Proceedings of the Second Pacific Rim Geometry Conference, J. Berrick, B. Loo, H.-Y. Wang (Editors), pp. 207-218, Walter de Gruyter Co., Berlin, New York, 1997.
  6. LEUNG, Man Chun: Conformal invariants of manifolds of non-positive scalar curvature, tex-file, postscript, Geometriae Dedicata, 66 (1997), 233-243.
  7. LEUNG, Man Chun: Rigidity of Einstein manifolds of nonpositive curvature, Differential Geometry and Its Applications 7 (1997), 181-192.
  8. Cheung L.-F., Law C.-K. LEUNG M.-C. & J. B. McLeod: Entire solutions of quasilinear differential equations corresponding to p-harmonic maps, Nonlinear Analysis 31 (1998), 701-715.
  9. LEUNG, Man Chun: Positive solutions of second order quasilinear equations corresponding to p-harmonic maps, Nonlinear Analysis 31 (1998), 717-733.
  10. LEUNG, Man Chun: Positive solutions of F-harmonic maps equations, Discrete and Continuous Dynamical Systems, Special Volume II (1998), Proceedings of the International Conference on Dynamical Systems and Differential Equations, 1996, Edited by Wenxiong Chen and Shouchuan Hu, pp. 73-86.
  11. Cheung, L.-F., Law C.-K. & LEUNG, M.-C.: Uniqueness of positive solutions to the rotationally symmetric p-harmonic map equations, Journal of Computational and Applied Math. 88 (1998), 45-56.
  12. LEUNG, Man Chun: Conformal deformation of warped products and scalar curvature functions on open manifolds, Bulletin des Sciences Mathematiques 122 (1998), 369-398.
  13. LEUNG, Man Chun: Positive solutions of quasilinear differential equations corresponding to F-harmonic maps, Nonlinear Analysis 35 (1999), 287-306.
  14. LEUNG, Man Chun: Asymptotic behavior of positive solutions to the equation $\Delta_g u + K u^p = 0$ in a complete Riemannian manifold and positive scalar curvature, Comm. Partial Differential Equations 24 (1999), 425-462.
  15. Cheung L.F., Law C.-K. & LEUNG M.-C.: Bounded positive solutions of rotationally symmetric harmonic maps equations , Differential and Integral Equations 13 (2000), 1149-1188.
  16. LEUNG, Man Chun: Unbounded positive solutions of rotationally symmetric harmonic maps equations , Comput. Math. Appl. 39 (2000), 9-20.
  17. LEUNG, Man Chun: Growth estimates on positive solutions of the equation $\Delta u + K u^{{n + 2}\over {n - 2}} = 0$ in $R^n$, Canad. Math. Bull. 44 (2001), 210-222.
  18. LEUNG, Man Chun: Boundedness of positive solutions of the conformal scalar curvature equation and positive scalar curvature, Comm. Partial Differential Equations 26 (2001), 285-293.
  19. LEUNG, Man Chun: Conformal scalar curvature equations in open spaces , Cubo 3 (2001), 415-443 (invited contribution).
  20. Cheung, K.-L. & LEUNG, M.-C.: Asymptotic behavior of positive solutions of the equation $\Delta u + K u^{{n + 2}\over {n - 2}} = 0$ in $R^n$ and positive scalar curvature , Discrete Contin. Dynam. Systems, Added Volume (Proceedings of the Third International Conference on Dynamical Systems and Differential Equations, Edited by Joshua Du and Shouchuan Hu) (2001), 109-120.
  21. LEUNG, Man Chun: Exotic solutions of the conformal scalar curvature equation in $R^n$ , Annales de l'Institut Henri Poincare - Analyse Non Lineaire, 18 (2001), 297-307.
  22. J. Berrick, M.-C. Leung, X.-W. Xu (Editors), Topology and Geometry: Commemorating SISTAG, Contemporary Math. Vol 314, American Mathematical Society, 2002 (263 pages).
  23. LEUNG, Man Chun: Blow-up solutions of nonlinear elliptic equations in R^n with critical exponent, Math. Ann. 327 (2003), 723-744. (an earlier version is available in math.AP/0202244 ).
  24. LEUNG, Man Chun: Combining solutions of semilinear partial differential equations in R^n with critical Sobolev exponent, Comm. Partial Differential Equations, 29 (2004), 763-784.
  25. LEUNG, Man Chun: Concentration of solutions of non-linear elliptic equations involving critical Sobolev exponent , Cubo 7 (2005), 1-21 (invited contribution).
  26. LEUNG, Man Chun: Perspectives on bubble analysis for critically nonlinear PDEs , A Festschrift in Honour of Professor M.-K. Siu, pp. 215-268, Hong Kong University, To Appear.
  27. LEUNG, Man Chun: Local properties on the prescribed scalar curvature problem on S^n, Preprint.
  28. LEUNG, Man Chun: Supported blow-up and prescribed scalar curvature on S^n, Preprint.
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Last Modified: 14 Feb, 2008.