Partial regularity of a minimizer of the relaxed energy for biharmonic maps

Friday, March 25, 2011 -
3:00pm to 5:00pm
In 1999, Chang, Wang and Yang established the fundamental result on the partial regularity stationary biharmonic maps into spheres. Since then, the study of biharmonic maps has attracted much attention. In this talk, we will discuss some new result on the relaxed energy for biharmonic maps from an $m$-dimensional domain into spheres for an integer $m\geq 5$. We prove that the minimizer of the relaxed energy of the Hessian energy is biharmonic and smooth outside a singular set $\Sigma$ of finite $(m-4)$-dimensional Hausdorff measure. Moreover, when $m=5$, we also show that the singular set $\Sigma$ is $1$-rectifiable.
Speaker: 
Min-Chun Hong
University of Queensland, Brisbane
Event Location: 
Fine Hall 314