Energy identity for approximate harmonic maps from surface to general targets

2016/03/03 by Wendong Wang, Dongyi Wei, Wang, Wendong +3
Computer Science · Mathematics · #Advanced Mathematical Modeling in Engineering #Analysis of PDEs (math.AP) #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Nonlinear Partial Differential Equations

paper · pdf · doi:10.48550/arxiv.1603.00990

openalex publication_date 2016/03/03 · openalex created_date 2019/06/27 · openalex updated_date 2026/07/28

Abstract

Let u_n be a sequence of mappings from a closed Riemannian surface M to a general Riemannian manifold N. If u_n satisfies \beno sup_n(‖∇ u_n‖_L²(M)+‖τ(u_n)‖_L^p(M))≤ Λ for some p>1, \eeno where τ(u_n) is the tension field of u_n, then there hold the so called energy identity and neckless property 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) but the energy identity fails.

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