Energy identity of harmonic map flows from surfaces at finite singular time
The understanding of the behavior of harmonic maps from compact Riemannian surfaces \((M,g)\) to Riemannian submanifolds \((N,h) \subset \mathbb{R}^n\) near a singular point \(T_0\) of finite time is a difficult open problem. In this framework, the authors give a different (simpler) proof of a theorem of Qing-Tian [\textit{J. Qing} and \textit{G. Tian}, Commun. Pure Appl. Math. 50, No. 4, 295-310 (1997; Zbl 0879.58017)]. Namely, they provide an energy identity for the harmonic flow \(u(\cdot,t)\), which involves a finite number of nonconstant harmonic maps \(\omega_i: S^2 \to N\) (referred to as bubbles) associated with \(u(\cdot,t)\).
scientific article; zbMATH DE number 1160794