Department of Mathematics
Texas A & M - Commerce
Student/Faculty Colloquium
Wednesday, September 30, 2009
Binnion 301, 2:00-2:50pm
Yelin Ou,
Texas A & M-Commerce
will speak on:
The Geometry of Biharmonic Maps
Abstract:
Biharmonic maps are transformations between two spaces that minimize the
bi-energy functional. Harmonic maps (e.g., geodesic, minimal surfaces,
and holomorphic functions) form a special subclass of biharmonic maps
so we call those non-harmonic biharmonic maps proper biharmonic maps.
Examples of proper biharmonic maps are extremely difficult to find.
In this talk, we will review some fundamental problems in the study of
biharmonic maps, some known examples of proper biharmonic maps, and we will
then present several methods that can be used to construct many new examples
of proper biharmonic maps including biharmonic tori of any dimension in spheres,
a family of biharmonic conformal immersions of cylinder into Euclidean 3-space,
a foliation of proper biharmonic hypersurface in a conformally flat space,
and some biharmonic maps between surfaces.