Energy identity for a class of approximate biharmonic maps into sphere in dimension four

2011/10/29 by Changyou Wang, Wang, Changyou, Shenzhou Zheng +1 · 1 citation
Mathematics · #Geometric Analysis and Curvature Flows #Geometry and complex manifolds #Mathematical Dynamics and Fractals

paper · pdf · doi:10.48550/arxiv.1110.6536

Abstract

We consdier in dimension four weakly convergent sequences of approximate biharmonic maos into sphere with bi-tension fields bounded in L^p for some p>1. We prove an energy identity that accounts for the loss of Hessian energies by the sum of Hessian energies over finitely many nontrivial biharmonic maps on \mathbb R⁴.

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