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

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

-
Min-Chun Hong, University of Queensland, Brisbane
Fine Hall 314

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.