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Chen Daguang (Tsinghua University) Fan Huijun (Peking University) Feng Huitao (Nankai University) Fu Jixiang (Fudan University) Futaki Akito (University of Tokyo) Guo Zhen (Yunnan Normal University) Kunikawa Keita (Nagoya University) Li Haizhong (Tsinghua University) Li Jiayu (University of Science and Technology of China Liu Xiaobo (Peking University) Mabuchi Toshiki (Osaka University) Saito Shunsuke (University of Tokyo) Tamaru Hiroshi (Hiroshima University) Tian Gang (Peking University and Princeton University) Xu Guangbo (Princeton University) Yamaguchi Takao (Kyoto University) Yan Wenjiao (Beijing Normal University) Zhang Weiping (Nankai University) Zhu Xiaohua (Peking University) Organizing Committee Cheng Qing-Ming (Fukuoka University), Sano Yuji (Fukuoka University)

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Energy identity for a sequence of Sacks-Uhlenbeckmaps to a sphere

Li, Jiayu

Abstract

For a map u from a Riemann surface M to a Riemannian manifold andα > 1, the α energy functional is defined as

Eα(u) =!M

|∇u|2αdx.

We call uα a sequence of Sacks-Uhlenbeck maps if uα is a critical point of Eα

andsupα>1

Eα(uα) < ∞.

In this talk, when the target manifold is a standard sphere SK , we provethe energy identity for a sequence of Sacks-Uhlenbeck maps during blowing up.

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