Jost Jürgen, Liu Lei, Zhu Miaomiao
1Max Planck Institute for Mathematics in the Sciences, Inselstrasse 22, 04103 Leipzig, Germany.
2Department of Mathematics, Leipzig University, 04081 Leipzig, Germany.
Math Ann. 2019;374(1):133-177. doi: 10.1007/s00208-018-1759-8. Epub 2018 Sep 24.
Let be a sequence of maps from a compact Riemann surface with smooth boundary to a general compact Riemannian manifold with free boundary on a smooth submanifold satisfying where is the tension field of the map . 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.
设({u_n})是一列从具有光滑边界的紧致黎曼曲面到一般紧致黎曼流形的映射，该流形在满足(\tau(u)=\vec{H})（其中(\tau(u))是映射(u)的张力场）的光滑子流形上具有自由边界。我们证明在一个爆破过程中能量恒等式和无颈性质成立。这些假设使得该结果也适用于具有自由边界的调和映射热流，以证明在有限奇异时间以及无穷时间的能量恒等式。此外，无颈性质在无穷时间成立。
