Energy identity of approximate biharmonic maps to Riemannian manifolds and its application

2011/12/29 by Wang, Changyou, Zheng, Shenzhou
#Analysis of PDEs (math.AP) #Differential Geometry (math.DG) #FOS: Mathematics

paper · doi:10.48550/arxiv.1112.6362

Abstract

We consider in dimension four weakly convergent sequences of approximate biharmonic maps to a Riemannian manifold with bi-tension fields bounded in L^p for p>\frac43. 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. As a corollary, we obtain an energy identity for the heat flow of biharmonic maps at time infinity.

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