Electron. J. Diff. Equ., Vol. 2013 (2013), No. 177, pp. 1-13.

Energy quantization for approximate H-surfaces and applications

Shenzhou Zheng

We consider weakly convergent sequences of approximate H-surface maps defined in the plane with their tension fields bounded in $L^p$ for p> 4/3, and establish an energy quantization that accounts for the loss of their energies by the sum of energies over finitely many nontrivial bubbles maps on $\mathbb{R}^2$. As a direct consequence, we establish the energy identity at finite singular time to their H-surface flows.

Submitted February 2, 2013. Published July 30, 2013.
Math Subject Classifications: 35J50, 35K40, 58D15.
Key Words: Approximate H-surface maps; energy quantization; H-surface flows; concentration of energy; bubbling phenomena.

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Shenzhou Zheng
Department of Mathematics, Beijing Jiaotong University
Beijing 100044, China
email: shzhzheng@bjtu.edu.cn, Phone: +86-10-51688449

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