Let u be a map from a Riemann surface M to a Riemannian manifold N and , the α energy functional is defined as
We call a sequence of Sacks–Uhlenbeck maps if are critical points of and
In this paper, we show the energy identity and necklessness for a sequence of Sacks–Uhlenbeck maps during blowing up, if the target N is a sphere . The energy identity can be used to give an alternative proof of Perelman's result  that the Ricci flow from a compact orientable prime non-aspherical 3-dimensional manifold becomes extinct in finite time (cf. [3,4]).
Cite this article
Jiayu Li, Xiangrong Zhu, Energy identity and necklessness for a sequence of Sacks–Uhlenbeck maps to a sphere. Ann. Inst. H. Poincaré Anal. Non Linéaire 36 (2019), no. 1, pp. 103–118DOI 10.1016/J.ANIHPC.2018.04.002