Energy identity for approximate harmonic maps from surfaces to general targets

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• 作者：Wendong Wang^a ; ^{wendong@dlut.edu.cn" class="auth_mail" title="E-mail the corresponding author} ; Dongyi Wei^b ; ^{jnwdyi@163.com" class="auth_mail" title="E-mail the corresponding author} ; Zhifei Zhang^c ; ^{zfzhang@math.pku.edu.cn" class="auth_mail" title="E-mail the corresponding author}
• 关键词：Energy identity ; Harmonic map ; Hopf differential
• 刊名：Journal of Functional Analysis
• 出版年：2017
• 出版时间：15 January 2017
• 年：2017
• 卷：272
• 期：2
• 页码：776-803
• 全文大小：435 K

文摘

Let u_n$u_n$ be a sequence of mappings from a closed Riemannian surface M to a general Riemannian manifold N  . If u_n$u_n$ satisfies where τ(u_n)$\tau (u_n)$ is the tension field of u_n$u_n$, then the so called energy identity and neckless property hold during blowing up. This result is sharp by Parker's example, where the tension fields of the mappings from Riemannian surface are bounded in L¹(M)$L^1(M)$ but the energy identity fails.