| I. Teaching (Spring
- General Topology I (M210; Friday,
- Tuesday: 8-10.
- Thursday: 8-10.
A. Research Interests
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
elastic networks: long-time existence result,
Preprint, 2018. (with Anna
Dall'Acqua, Paola Pozzi).
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. (with Yang-Kai Lue).
elastic flow of curves on the sphere, Geometric
Flows, Vol. 3, no. 1, pp.
1-13, 2018. (with Anna Dall'Acqua, Tim Laux,
Paola Pozzi, Adrian Spener)
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. (with Anna Dall'Acqua and
of open elastic curves in R^n subject to fixed
length and natural boundary conditions. Analysis
34 (2014), no. 2, 209-222 (with Anna
Dall'Acqua and Paola Pozzi).
continuity of two-dimensional weakly
stationary-harmonic multiple-valued functions.
Geom. Anal., 24 (2014), no. 3,
of elastic curves with clamped boundary
Differential Equations, 252
(2012), no. 12, 6414-6428.
On a flow
to untangle elastic knots. Calc.
Var. Partial Differential Equations,
39 (2010), no. 3-4, 621-647 (with Hartmut R.
Evolving a Kirchhoff elastic rod
without self-intersections. J.
Math. Chem., 45 (2009), no. 3,
748-768 (with Hartmut R. Schwetlick).
generalized Bertrand curves in Euclidean
di Matematica, 29 (2009), no. 2,
33-39 (with Yung-Ming Cheng).
geometric flow of Kirchhoff elastic rods. SIAM J. on Appl. Math., 65 (2005), no. 2,
720-736 (with Hartmut R.
Rigidity for the
hyperbolic Monge-Ampere equation. Ann.
Sc. Norm. Super. Pisa Cl. Sci.,
(5) 3 (2004), no. 3, 609-623.
Negatively curved sets on
surfaces of constant mean curvature in R^3
Arch. for Rational Mech. Anal.,
141 (1998), no. 2, 105-116 (with
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
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.
elastic knots, (in preparation).
using bending energy+knot
energy: (i) (9,1)-unknot
zipped file), (ii) (1,20)-unknot
zipped file), (iii)
zipped file), (iv) (2,3)-knot
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
zipped file), (ii) almost
planar figure-8 (or its
zipped file). Notice that
self-intersection might happen during this
knid of evolution.
Turning a torus inside out, (in
E. Popular Sciences