Chun-Chi Lin
Department of Mathematics, National Taiwan Normal University, Taipei, 116 Taiwan
  • Office Phone : +886-(0)2-7749-6621, Fax : +886-(0)2-29332342.
  • Email: chunlin "at" math.ntnu.edu.tw 
I. Teaching:
  • Courses 
  1. 2024 Fall: Advanced Calculus (I) (Tuesday+Thursday, 9:10-12:10).
  2. 2024 Fall: Topics in Differential Geometry (II) (Wednesday 3:30-18:20).
  • Office Hours
  1. Wednesday: 10-12 (M221).
  2. Friday: 10-12 (M221).
  3. by appointment.

II. Research:

A. Research Interests

My research focuses on nonlinear variational problems motivated from differential geometry, mechanics, quantum computations, or biology. The mathematical issues of these variational problems include existence, regularity theory, geometric singularities, and dynamic behaviour. In addition, I am interested to see applications of rigorous mathematics in natural sciences.

B. Journal Articles     

  • C.-C. Lin, Y.-K. Lue, D. T. Tran, A second-order elastic flow for path planning in R^2, Commun. Contemp. Math., 26 (2024), no. 4, Paper No. 2250080, 34 pp.
  • C.-C. Lin, H. R. Schwetlick, Dung The Tran, An elastic flow for nonlinear spline interpolations in R^n, Transactions Amer. Math. Soc., Vol. 375, No. 7, pp. 4893-4942, July 2022. 
  • NSCM Dall'Acqua, C.-C. Lin, P. Pozzi, Elastic flow of networks: short-time existence result, J. Evolution Eq., Vol. 21, No. 2, pp. 1299-1344, 2021.
  • Dall'Acqua, C.-C. Lin, P. Pozzi, Elastic flow of networks: long-time existence result, Geometric Flows, Vol. 4, No. 1, pp. 83-136, 2019.
  • T. L. J. Harris, B. Kirchheim, C.-C. Lin, Two-by-two upper triangular matrices and Morrey's conjecture, Calc. Var. Partial Differential Equations, 57 (2018), No. 3, pp. 57-73.
  • A. Dall'Acqua, T. Laux,  C.-C. Lin, P. Pozzi, A. Spener, The elastic flow of curves on the sphere, Geometric Flows, Vol. 3, No. 1, pp. 1-13, 2018.
  • C.-C. Lin, Y.-K. Lue, Evolving inextensible and elastic curves with clamped ends under the second-order evolution equation in R^2, Geometric Flows, Vol. 3, No. 1, pp. 14-18, 2018.
  • Dall'Acqua, C.-C. Lin, P. Pozzi, A gradient flow for open elastic curves with fixed length and clamped ends, Ann. Sc. Norm. Super. Pisa Cl. Sci., Vol. 5, No. 17, pp. 1031-1066, 2017.
  • C.-C. Lin, Y.-K. Lue, H. R. Schwetlick, The second-order L^2-flow of inextensible elastic curves with hinged ends in the plane, J. Elasticity, 119 (2015), No. 1, 263-291.
  • C.-C. Lin, Interior continuity of two-dimensional weakly stationary-harmonic multiple-valued functions, J. Geom. Anal. 24 (2014) No. 3, 1547-1582.
  • A. Dall'Acqua, C.-C. Lin, P. Pozzi, Evolution of open elastic curves in R^n subject to fixed length and natural boundary conditions, Analysis (Berlin), Vol. 34, No. 2, pp. 209-222, 2014.
  • C.-C. Lin, L^2-flow of elastic curves with clamped boundary conditions, J. Differential Eq., 252 (2012), No. 12, 6414-6428.
  • C.-C. Lin, H. R. Schwetlick, On a flow to untangle elastic knots, Calc. Var. Partial Differential Equations, 39, 2010, No. 3-4, 621-647.
  • Y.-M. Cheng, C.-C. Lin, On the generalized Bertrand curves in Euclidean N-spaces, Note di Mate., Vol. 29, No. 2, pp.33-39, 2009.
  • C.-C. Lin, H. R. Schwetlick, Evolving a Kirchhoff elastic rod without self-intersections, J. Math. Chem., Vol. 45, No. 3, pp. 748-768, 2009.
  • C.-C. Lin, H. R. Schwetlick, On the geometric flow of Kirchhoff elastic rods,  SIAM J. Applied Math., 65, 2005, No. 2, 720-736.
  • C.-C. Lin, Rigidity for the hyperbolic Monge-Ampere equation, Ann. Sc. Norm. Super. Pisa Cl. Sci., (5) Vol. III, 2004, No. 3, pp. 609-623.
  • W. H. Huang, C.-C. Lin, Negatively curved sets on surfaces of constant mean curvature in R^3 are large, Arch. Rational Mech. Anal., 141, 1998, No. 2, pp. 105-116.
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    C. Conference Articles  

  • How can the game of Hex be used to inspire students in learning mathematical reasoning?, Proceedings of the ICMI Study 19 Conference, Vol. 2, 2009, p. 37-40, ISBN 978-986-01-8210-1.

  • Finding the elasticae by means of geometric gradient flows, Recent advances in elliptic and parabolic problems, p. 189-196, World Sci. Publ., Hackensack, NJ, 2005, ISBN 978-981-256-189-3 (with Hartmut Schwetlick).

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    D. Movies and Animations  

  • Untangling elastic knots (click here for the poster): Below are movie files in which torus knots evolving by the gradient flow of energies.
    •

        1. using bending energy+knot energy: (i) (9,1)-unknot (or its zipped file), (ii) (1,20)-unknot (or its zipped file), (iii) (2,3)-unknot (or its zipped file), (iv) (2,3)-knot (or its zipped file), (v) almost planar figure-8 (or its zipped file). Notice that all unknots above evolve into round circles;

        2. using bending energy only: (i) (2,3)-knot (or its zipped file), (ii) almost planar figure-8 (or its zipped file). Notice that self-intersection might happen during the kind of evolution.


    E. Popular Sciences