



I. Teaching (Spring
Semester 2019):
 General Topology I (M210; Friday,
9:1012:00).
 Tuesday: 810.
 Thursday: 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
Flow of
elastic networks: longtime existence result,
ArXiv
Preprint, 2018. (with Anna
Dall'Acqua, Paola Pozzi).
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. (with YangKai Lue).
The
elastic flow of curves on the sphere, Geometric
Flows, Vol. 3, no. 1, pp.
113, 2018. (with Anna Dall'Acqua, Tim Laux,
Paola Pozzi, Adrian Spener)
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. (with Anna Dall'Acqua and
Paola Pozzi).
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

