arXiv subjects

Shenzhou Zheng

Publications and source records attributed to Shenzhou Zheng.

2 recordsLinked to original sources

arXiv2011

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

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 $\mathbb R^4$. As a corollary, we obtain an energy identity for the heat flow of biharmonic maps at time infinity.

math.AP↗

arXiv2011

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

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 $\mathbb R^4$.

math.AP↗