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I. Teaching:
II.
Research:
A. Research Interests
My research
interests focus mainly on nonlinear variational
problems motivated from differential geometry,
physical sciences and applied sciences. The
mathematical issues include existence, (partial)
regularity theory, local behavior of
solutions around singularities and their
structures, dynamics related to these
variational problems. In addition, I am
interested in applications of rigorous
mathematics in sciences.
B. Journal Articles
C.-C. Lin and H.
R. Schwetlick, L^2-flow of elastic curves with
knot points and clamped ends, Submitted 2012.
C.-C. Lin, Interior continuity of
two-dimensional weakly stationary-harmonic
multiple-valued functions, J.
Geometric Analysis (to appear 2013).
C.-C. Lin, L^2-flow of elastic curves
with clamped boundary conditions, J.
Differential Equations, 252 (2012), no.
12, 6414-6428.
C.-C. Lin and H. R. Schwetlick, On a flow
to untangle elastic knots, Calc.
Var. Partial Differential Equations, 39,
2010, no. 3-4, 621-647.
C.-C.
Lin and H. R. Schwetlick, Evolving a
Kirchhoff elastic rod without
self-intersections, J.
Math. Chem., 45, 2009, no.
3, 748-768.
Y.-M. Cheng and C.-C. Lin, On the
generalized Bertrand curves in Euclidean
N-spaces, Note
di Matematica, 29 (2), 2009,
33-39.
C.-C.
Lin and H. R. Schwetlick, On the geometric
flow of Kirchhoff elastic rods, SIAM J. on Appl. Math., 65, 2005, no. 2,
720-736.
C.-C. Lin, Rigidity for
the hyperbolic Monge-Ampere equation,
Annali della Scuola Normale Superiore
di Pisa Classe di Scienze, (5)
Vol. III, 2004, no. 3, pp. 609-623.
W.-H. Huang and C.-C.
Lin, Negatively curved sets on surfaces of
constant mean curvature in R^3 are large,
Arch. for Rational Mech. Anal.,
141, 1998, no. 2, 105-116.
C. Conference Articles
C.-C. Lin, 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.
C.-C. Lin
and H. R. Schwetlick, 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.
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 figure-8 (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 figure-8 (or its
zipped file). Notice
that self-intersection might happen
during this knid of evolution.
Tangling
elastic knots, (in preparation).
Turning a torus inside out, (in
preparation).
E. Popular Sciences
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