题   目: The qualitative behavior at the free boundary for approximate harmonic maps from surfaces

报告人： 刘磊    (Max Planck Institute, German) 

摘    要: Let $\{u_n\}$ be  a sequence of maps from a compact Riemann surface $M$ with smooth boundary to a general compact Riemannian manifold $N$ with free boundary on   a smooth submanifold $K\subset N$ satisfying

\[

\sup_n(\|\nabla u_n\|_{L^2(M)}+\|\tau(u_n)\|_{L^2(M)})\leq \Lambda,

\]

where  $\tau(u_n)$ is the tension field of the map $u_n$. We show that the energy identity and the no neck property hold during a blow-up process. The assumptions are such that this result also applies to the harmonic map heat flow  with free boundary, to prove the energy identity at finite singular time as well as at infinity time. Also, the no neck property holds at infinity time.

时   间： 2018年3月21日 14:00--16:00

地   点：蒙民伟楼1105室

邀请人：陈学长 老师