6 papers
Images of Harmonic Maps with Symmetry
Thomas Kwok-keung Au, Tom Yau-heng Wan
We show that under certain symmetry, the images of complete harmonic embeddings from the complex plane into the hyperbolic plane is completely determined by the geometric informati…
Hopf Differentials and the Images of Harmonic Maps
Thomas Kwok-keung Au, Luen-fai Tam, Tom Yau-heng Wan
Non-polynomial growth harmonic maps from the complex plane to the hyperbolic space are studied. Some non-surjectivity results are obtained. Moreover, images of such harmonic maps a…
An Analysis on the Shape Equation for Biconcave Axisymmetric Vesicles
Thomas Kwok-keung Au, Tom Yau-heng Wan
We study the conditions on the physical parameters in the Helfrich bending energy of lipid bilayer vesicles. Among embedded surfaces with a biconcave axisymmetric shape, the variat…
The Dynamics of Off-center Reflection
Thomas Kwok-keung Au
The dynamical properties, especially the symmetric orbits, of the 2-parameter family of circle maps called off-center reflection is studied.
Conditions for the Formation of Axisymmetric Biconcave Vesicles
Thomas Kwok-keung Au, Tom Yau-heng Wan
In this article, the formation of biconcave vesicle according to the minimization bending energy (Helfrich's model) is studied. We present that in order to have biconcave shape ves…
Off-center Reflections: Caustics and Chaos
Thomas Kwok-keung Au, Xiao-song Lin
In this article, we attempt to study the possible link between the dynamics of a circle map and the caustics of its iterations. The attention is on a geometrically defined off-cent…