



I. Teaching:
 2022 Fall: Riemannian Geometry I (M310
and/or Online; Tuesday, 9:1012:10).
 2023 Spring: Riemannian Geometry II (M310
and/or online; Tuesday 9:1012:10).
 Thursday: 1012 (M221 and/or Online 
wonder.me).
 Friday: 1517 (M221 and/or Online
wonder.me).
 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
secondorder elastic flow for path planning in
R^2, Commun. Contemp. Math., to appear 2023.
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.
48934942, July 2022.
NSCM
Dall'Acqua, C.C. Lin, P. Pozzi, Elastic flow
of networks: shorttime existence result, J.
Evolution Eq., Vol. 21, No. 2, pp.
12991344, 2021.
Dall'Acqua, C.C. Lin, P.
Pozzi, Elastic flow of networks: longtime
existence result, Geometric Flows,
Vol. 4, No. 1, pp. 83136, 2019.
T. L. J. Harris, B. Kirchheim,
C.C. Lin, Twobytwo upper triangular
matrices and Morrey's conjecture, Calc.
Var. Partial Differential Equations, 57
(2018), No. 3, pp. 5773.
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. 113, 2018.
C.C. Lin, Y.K. Lue, Evolving
inextensible and elastic curves with clamped
ends under the secondorder evolution equation
in R^2, Geometric Flows, Vol. 3, No.
1, pp. 1418, 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. 10311066, 2017.
C.C. Lin, Y.K. Lue, H. R.
Schwetlick, The secondorder L^2flow of
inextensible elastic curves with hinged ends
in the plane, J. Elasticity, 119
(2015), No. 1, 263291.
C.C. Lin, Interior continuity
of twodimensional weakly stationaryharmonic
multiplevalued functions, J. Geom. Anal.
24 (2014) No. 3, 15471582.
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. 209222, 2014.
C.C. Lin, L^2flow of elastic
curves with clamped boundary conditions, J.
Differential Eq., 252 (2012), No. 12,
64146428.
C.C. Lin, H. R. Schwetlick,
On a flow to untangle elastic knots, Calc.
Var. Partial Differential Equations, 39,
2010, No. 34, 621647.
Y.M. Cheng, C.C. Lin, On the
generalized Bertrand curves in Euclidean
Nspaces, Note di Mate., Vol. 29, No. 2,
pp.3339, 2009.
C.C. Lin, H. R. Schwetlick,
Evolving a Kirchhoff elastic rod without
selfintersections, J. Math. Chem., Vol. 45,
No. 3, pp. 748768, 2009.
C.C. Lin, H. R. Schwetlick,
On the geometric flow of Kirchhoff elastic
rods, SIAM J. Applied Math., 65,
2005, No. 2, 720736.
C.C. Lin, Rigidity for the
hyperbolic MongeAmpere equation, Ann. Sc.
Norm. Super. Pisa Cl. Sci., (5) Vol.
III, 2004, No. 3, pp. 609623.
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. 105116.
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. 3740, ISBN 9789860182101.
Finding the
elasticae by means of geometric gradient
flows, Recent advances in elliptic and
parabolic problems, p. 189196, World Sci.
Publ., Hackensack, NJ, 2005, ISBN
9789812561893 (with
Hartmut Schwetlick).
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.

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 figure8 (or its
zipped file). Notice
that all unknots above evolve into round
circles;

using bending energy only: (i) (2,3)knot
(or its
zipped file), (ii) almost
planar figure8 (or its
zipped file). Notice
that selfintersection might happen
during the kind of evolution.
E. Popular Sciences

