Chang-Shou Lin





Degree InstitutionĦG

Ph.D. in Mathematics, Courant Institute of Mathematical Sciences, New York University

Specialized AreasĦG

Differential Geometry,
Partial Differential Equations


(886)5-272-0411 ext 66116






A. Publications

  1. Lin, C.S.ĦA1985ĦAThe Local Isometric Embeddings in R^3 pf Two-Dimensional Riemannian Manifolds with nonnegative curvatureĦAJ. of Differential Geometry, 21 (1985), 213-230.

  2. Lin, C.S.ĦA1986ĦA The Local Isometric Embedding in R^3 of Two-dimensional Riemannian Manifolds with Gaussian curvature changing Sign CleanlyĦA Communication on Pure and Applied Mathematics, 39 (1986), 867-887.

  3. Lin, C.S.ĦA1986ĦA Interpolation Inequalities with WeightsĦAComm. in Partial Differential Equations, 11 (1986), 1515-1538.

  4. Lin, C.S.ĦA1987ĦAOn the Second Eigenfunctions of the Laplacian in R^2 ĦAComm. Math. Phys. 111 (1987), 161-166.

  5. Lin, C.S., Ni, W.M. and Takagi, I.ĦA1988ĦA Large Amplitude Stationary Solutins to a Chemotaxis SystemĦA J. of Differential Equation, 72 (1988), 1-27.

  6. Lin, C.S. and Ni, W.M.ĦA1988ĦA A Counterexample to the Nodal Domain Conjecture and a Related Semilinear EquationĦAProceeding of AMS, 102 (1988), 271-278.

  7. Lin, C.S. and Ni, W.M.ĦA1988ĦAOn the Diffusion Coefficient of a Semilinear Neumann ProblemsĦAIn Lecture Notes in Mathematics, Vol. 1340, 1988, pp.160-174. Ed. by Hildebrandt, Kinderlehrer and Miranda.

  8. Lin, C.S. and Tso, K.S.ĦA1990ĦA On Regular Solutions of Second Order Degenerate Elliptic-parabolic EquationsĦAComm. in Partial Differential Equations. 15 (1990), 1329-1360.

  9. Chen, C.C. and Lin, C.S.ĦA1991ĦA Uniqueness of Ground State Solutions of Ħµu+f(u)=0 in R^2, nĦÙ3ĦAComm. in Partial Differential Equations,16 (1991), 1549-1572.

  10. Chen, C.C. and Lin, C.S.ĦA1995ĦA Local Behavior of Singular Positions of Semilinear Elliptic Equations with Sobolev ExponentĦA Duke Math. Journal 78 (1995), 315-334.

  11. Lin, C.S.ĦA1997ĦANon-existence of Positive Solutions of Scalar Curvature Equation in R^n ĦAsubmitted

  12. Chen, C.C. and Lin, C.S.ĦA1997ĦAOn Boundedness of Positive Solutions of Scalar Curvature Equations in R^n, ĦAsubmitted

  13. Cheng, K.S. and Lin, C.S.ĦA1997ĦAOn the Asymptotic Behavior of Solutions of the Conformal Gaussian Curvature Equations in R^2ĦAMath. Ann., 308 (1997), 119-139.

  14. Chen, C.C. and Lin, C.S.ĦA1997ĦA Estimates of the Conformal Scalar Curvature Equation Via the Method of Moving Planes ĦAComm. Pure Appl. Math., 50 (1997), 971-1017.

  15. Chen, C.C. and Lin, C.S.ĦA1997ĦA On Completeness and Compactness of Conformal Metrics in R^nĦAAsian J. of Math., 1 (1997), 565-575.

  16. Cheng, K.S., and Lin, C.S.ĦA1998ĦA On the Conformal Gaussian Curvature Equations in R^2ĦA J. Differential Equations, 146 (1998), 226-250.

  17. Chen, C.C. and Lin, C.S.ĦA1998ĦA Estimate of the Conformal Scalar Curvature Equation Via the Method of Moving Planes, IIĦAJournal of Differential Geometry, 49(1998), 115-178.

  18. Lin, C.S.ĦA1998ĦAA Classification of Solutions of a Conformally Invariant Fourth Order Equation in R^nĦACommentarii Mathematici Helvetici, 73 (1998), 206-231.

  19. Cheng, K.S. and Lin, C.S.ĦA1998ĦA Compactness of Conformal Metrics with Positive Gaussian Curvature in R^2ĦAAnn. Scuola. Norm. Sup. Pisa, Ser. IV, 26(1998), 31-45.

  20. Lin, C.S.ĦA1998ĦALiouville-type Theorems for Semilinear Elliptic Equations Involving the Sobolev Exponent723-744. ĦAMathematische Zeitschrift, 228 (1998),

  21. Chen, C.C. and Lin, C.S.ĦA1998ĦAA Sharp sup+inf Inequality for a Nonlinear Ellptic Equation in R^2ĦA Communication in Analysis and Geometry, 6 (1998), 1-19.

  22. Lin, C.S.ĦA1999ĦAOn Liouville Theorem and a Priori Estimate for the Scalar Curvature EquationsĦA Ann. Scuola. Norm. Sup. Pisa, Cl. Sci. (4), 27(1998), no. 1, 107-130, 1999.

  23. Chen, C.C. and Lin, C.S.ĦA1999ĦAOn the Asymptotic Symmetry of Singular Solutions of the Conformal Scalar Curvature EquationsĦAMath. Annallen, 313 (1999), 229-245.

  24. Cheng, K.S. and Lin, C.S.ĦA1999ĦAConformal Metrics in R^2 with Prescribed Gaussian Curvature with Positive Total Curvature in R^2 ĦANonlinear Analysis 38 (1999), no. 6, Ser. A: Theory methods, 775-783.

  25. Chen, C.C. and Lin C.S.ĦA1999ĦA Blowing up with Infinite Energy of Conformal Metrices on s^nĦAComm. in Partial Differential Equations, 24(1999), 785-799.

  26. Chen, C.C. and Lin, C.S.ĦA1999ĦAExistence of Positive Weak Solutions with a Prescribed Singular Set of a Semilinear Elliptic EquationĦAThe Journal of Geometric Analysis, 9(1999), 221-246.

  27. Guan, P.F. and Lin, C.S.ĦA2000ĦAOn Equation det(uij+£_iju)=u^pf on S^n,ĦApreprint, 2000

  28. Lin, C.S.ĦA2000ĦA Topological Degree for Mean Field Equations on S^2ĦA Duke Math. Journal, 104(2000), 501-536.

  29. Lin, C.S.ĦA2000ĦA Uniqueness of Solutions to the Mean Field Equation for the Spherical Onsager VortexĦAArch. for Rational Mechanics, 153(2000)2, 153-176.

  30. Cheng, K.S. and Lin, C.S.ĦA2000ĦA Conformal Metrics with Negative Gaussian Curvature in R^2ĦACalculus of Variations & PDE, 11(2000), 203-231.

  31. Cheng, K.S. and Lin, C.S.ĦA2000ĦAMultiple Solutions of Conformal Metrics with Negative Total CurvatureĦA Advances in Differential Equations, 5(2000), 1253-1288.

  32. Lin, C.S.ĦA2000ĦAUniqueness of Conformal Metrics with Prescribed Total Curvature in R^2ĦACalculus of Variations & PDE, 10(2000), 291-319.

  33. Lin, C.S.ĦA2000ĦAEstimates of the Scalar Curvature Equation Via the Method of Moving Planes, IIIĦA Communication on Pure and Applied Math., 53(2000), 611-646.

  34. Chen, C.C. and Lin, C.S.ĦA2000ĦABlowup behavior of mean field type equationsĦA Taiwanese J. of Math., 4(2000), 21-31.

  35. Chen, C.C. and Lin, C.S.ĦA2000ĦA On Axisymmetric Solutions of Conformal Scalar Curvature Equation on S^nĦAAdvances in Differential Equations, 5(2000), 121-147.

  36. Lin, C.S., and Wei, J.C.ĦA2001ĦAUniqueness of Multi-spike Solutions Via the Method of Moving PlanesĦApreprint, 2001.

  37. Grossi, Massimo, Lin, C. S. and Parashanth, S.ĦA2001ĦA A Uniqueness Result for a Neumann Problem Involving the Critical Sobolev ExponentĦAsubmitted, 2001.

  38. Chen, C.C. and Lin, C.S.ĦA2001ĦAOn Prescribing Scalar Curvature on S^n, Part I: Apriori EstimatesĦAJournal of Differential Geometry,57(2001), No.1, 67-171.

  39. Chen, C.C. and Lin, C.S.ĦA2001ĦA Spherical Harnack Inequality for Singular Solutions of Nonlinear Elliptic EquationĦA Ann. Scuola. Norm. Sup. Pisa, Cl. Sci (4), 30(2001), 713-738.

  40. Lin, C.S. and Takagi, I.ĦA2001ĦA Method of Rotating Planes Applied to a Singularly Perturbed Neumam Problems ĦA Calc. Var. and Partial Diff.Eqs., 12(2001), No. 4, 519-536.

  41. Lin, C.S.ĦA2001ĦALocating the Peaks of Solutions to a Neumann Problem Via the Maximum Principle, I: The Neumann Problem,ĦAComm. Pure Appl. Math., 56(2001), 1065-1095.

  42. Chen, C.C. and Lin, C.S.ĦA2001ĦAOn the Symmetry of Blowup Solutions to a Mean Field EquationĦAAnn. Linstitute H. Poincare', Analyse Nonline'are, 18, 3(2001), 271-296.

  43. Lin, C.SĦA2002ĦA The Existence of Multi-bubbling Solutions for the Spherical Onsager Vortex.ĦAIn preparation.

  44. Lin, C.S.ĦA2002ĦAUniqueness of Conformal Matrices on S^2.ĦAIn preparation

  45. Guan, P.F., Lin, C.S. and Ma, X.ĦA2002ĦAOn the Convexity and the Existence of Weigarten HypersurfacesĦA Preprint

  46. Han, Q., Hang, J.X. and Lin, C.S.ĦA2002ĦALocal Isometric Embedding of Surfaces with Nonpositive Gaussian Curvature ĦAsubmitted

  47. Lin, C.S. and Wei, J.C.ĦA2002ĦALocating the Peaks of Solutions Via the Maximum Principle, II: A Local Version of the Method of Moving Planes, ĦAsubmitted 2002.

  48. Chen, C.C. and Lin, C.S.ĦA2002ĦA On Prescribing Scalar Curvature on S^n, Part II: Counting the Leray Schauder Degree. ĦAIn preparation

  49. Chen, C.C. and Lin, C.S.ĦA2002ĦAA mean field Equation on Torus and the Weierstrass £^-function, A volume to be in honor of Professor Liouis Nirenberg on his seventy-five birthdayĦAto appear

  50. Chen, C.C. and Lin, C.S.ĦA2002ĦATopological Degree Mean for Field Equations on Riemann Surfaces ĦAsubmitted 2002

  51. Chan, H., Fu, C.C. and Lin, C. S.ĦA2002ĦA Non -topological Solutions to the self-dual Chern-Simons-Higgs equationĦAComm. Mahtematical Physics, to appear.

  52. Chang, S. Y. A., Chen, C. C. and Lin, C. S.ĦA2002ĦAExtremal Functions for a Mean Fiels Equation in Two DimesionĦAsubmitted

  53. Chen, C.C. and Lin, C.S.ĦA2002ĦASharp Estimates for Solutions with Multi-bubbles in Compact Riemann SurfaceĦAComm. Pure Appl. Math. 55(2002), 728-771.

  54. Han, Q., Hong, J.X. and Lin, C.S.ĦA2002ĦA Small Divisors in Nonlinear Elliptic Equations ĦACalc. Var. and PDE, to appear.

  55. Chern, J.L. and Lin, C.S.ĦA2002ĦA Axial Symmetry of the Least-energy Solutions of Nonlinear Elliptic Equations, Journal of Differential Equations,ĦA to appear.

  56. Gui, C.-F. and Lin, C.S.ĦA2002ĦA Estimates for Boundary-bubbling Solutions to an Elliptic Neumann ProblemĦAJ. fuĦ¨r die Reine und Angewandte Math. (Crelle J.), 546(2002), 201-235.

  57. Lin, C.S. and Zhu, X.H.ĦA2002ĦA Explicit Construction of Extremal Hermitian Metrics with Finite Singularities on S^2ĦAComm. Analysis and Geometry, 10(2002), No. 1, 177-216.

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