Dirac-harmonic maps from degenerating spin surfaces. I: The Neveu-Schwarz case (Q1017977)

Dirac-harmonic maps were introduced by \textit{Q. Chen, J. Jost, J. Y. Li}, and \textit{G. Wang} [Math. Z. 254, No. 2, 409--432 (2006; Zbl 1103.53033)]. In the present paper the author considers such maps from degenerating spin surfaces with uniformly bounded energy, and investigates a generalized bounded energy density when the domain converges to a spin surface having only Neveu-Schwarz type nodes. A necessary and sufficient condition for the \(W^{1,2}\times L^4\) modulo bubbles compactness of a sequence of such maps is found. Contents include: Introduction; Notation and preliminaries; Dirac-harmonic maps from spin cylinders; Dirac-harmonic maps from degenerating spin surfaces; and References (twenty-two items).