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Quantization for a nonlinear Dirac equation


Author: Miaomiao Zhu
Journal: Proc. Amer. Math. Soc. 144 (2016), 4533-4544
MSC (2010): Primary 58J05, 53C27
DOI: https://doi.org/10.1090/proc/13041
Published electronically: March 17, 2016
MathSciNet review: 3531200
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Abstract: We study solutions of certain nonlinear Dirac-type equations on Riemann spin surfaces. We first improve an energy identity theorem for a sequence of such solutions with uniformly bounded energy in the case of a fixed domain. Then, we prove the corresponding energy identity in the case that the equations have constant coefficients and the domains possibly degenerate to a spin surface with only Neveu-Schwarz type nodes.


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Miaomiao Zhu
Affiliation: Max Planck Institute for Mathematics in the Sciences, Inselstr. 22, D-04103 Leipzig, Germany
Address at time of publication: Department of Mathematics, Shanghai Jiao Tong University, Dongchuan Road 800, Shanghai 200240, People’s Republic of China
Email: mizhu@sjtu.edu.cn

DOI: https://doi.org/10.1090/proc/13041
Keywords: Dirac equation, energy identity, Neveu-Schwarz.
Received by editor(s): July 9, 2015
Received by editor(s) in revised form: November 20, 2015
Published electronically: March 17, 2016
Communicated by: Guofang Wei
Article copyright: © Copyright 2016 American Mathematical Society

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