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吴文俊数学重点实验室讲座【刘磊】
报告题目:The qualitative behavior at the free boundary for approximate harmonic maps from surfaces
 
报告人:  刘磊Max-planck institut fur mathematik In den naturwissenschaft, Leipzig, Germany

报告时间:6月23日 4:00-5:00

报告地点:管理科研楼 1518
 
 
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.
This is a joint work with Prof. Jurgen Jost and Prof. Miaomiao Zhu.
中国科学院吴文俊数学重点实验室