Energy identity and necklessness for a sequence of Sacks–Uhlenbeck maps to a sphere

  • Jiayu Li

    College of Mathematical Sciences, University of Science and Technology of China, Hefei 230026, PR China; AMSS, CAS, Beijing 100190, PR China
  • Xiangrong Zhu

    Department of Mathematica, Zhejiang Normal University, Jinhua 321004, PR China
Energy identity and necklessness for a sequence of Sacks–Uhlenbeck maps to a sphere cover
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Abstract

Let be a map from a Riemann surface to a Riemannian manifold and , the 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 is a sphere . The energy identity can be used to give an alternative proof of Perelman's result [15] 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. 103–118

DOI 10.1016/J.ANIHPC.2018.04.002