



I. Teaching (Spring
Semester 2016):
 Differential Geometry II (M210;
Friday, 2:004:40).
 Nonlinear Analysis II (M210; Tuesday,
4:305:20 & Wednesday, 10:3012:10).
 Wednesday: 810.
 Friday: 810.
II.
Research:
A. Research Interests
My
research focuses on nonlinear variational
problems motivated from differential geometry,
mechanics, material sciences or biology. The
mathematical issues of these variational
problems include existence, regularity theory,
geometric singularities, qualitative
properties, and dynamic behaviour. In addition,
I am interested to see applications of rigorous
mathematics in sciences.
B. Journal Articles
A gradient flow for open elastic curves
with fixed length and clamped ends. Ann.
Sc. Norm. Super. Pisa Cl. Sci.,
(accepted,
2016) (with Anna Dall'Acqua and Paola
Pozzi).
The secondorder L^2flow of
inextensible elastic curves with hinged ends
in the plane. J.
Elasticity, 119
(2015), no. 1, 263291.
(with YangKai Lue and Hartmut R. Schwetlick).
Evolution of open elastic curves in R^n
subject to fixed length and natural boundary
conditions. Analysis
(Berlin),
34 (2014), no. 2, 209222 (with Anna
Dall'Acqua and Paola Pozzi).
Interior continuity of twodimensional
weakly stationaryharmonic
multiplevalued functions. J.
Geom. Anal., 24 (2014),
no. 3, 15471582.
L^2flow of elastic curves with clamped
boundary conditions. J.
Differential Equations, 252
(2012), no. 12, 64146428.
On a flow to untangle elastic knots. Calc.
Var. Partial Differential Equations,
39 (2010), no. 34, 621647 (with Hartmut R.
Schwetlick).
Evolving
a Kirchhoff elastic rod without
selfintersections. J.
Math. Chem., 45
(2009), no. 3, 748768 (with
Hartmut R. Schwetlick).
On the generalized Bertrand curves in
Euclidean Nspaces. Note
di Matematica, 29 (2009),
no. 2, 3339 (with YungMing Cheng).
On the
geometric flow of Kirchhoff elastic rods. SIAM J. on Appl. Math., 65 (2005), no. 2,
720736 (with Hartmut R.
Schwetlick).
Rigidity for the
hyperbolic MongeAmpere equation. Ann.
Sc. Norm. Super. Pisa Cl. Sci.,
(5) 3 (2004), no. 3, 609623.
Negatively curved sets
on surfaces of constant mean curvature in
R^3 are large.
Arch. for Rational Mech. Anal.,
141 (1998), no. 2, 105116 (with
WuHsiung Huang).
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 this knid of evolution.
Tangling
elastic knots, (in preparation).
Turning a torus inside out, (in
preparation).
E. Popular Sciences

