Dirac-harmonic maps from degenerating spin surfaces I: the Neveu-Schwarz case

Abstract

We study Dirac-harmonic maps from degenerating spin surfaces with uniformly bounded energy and show the so-called generalized energy identity in the case that the domain converges to a spin surface with only Neveu-Schwarz type nodes. We find condition that is both necessary and sufficient for the $W^{1,2}\times L^4$ modulo bubbles compactness of a sequence of such maps.

24 pages

References in corpus (1)

• Harmonic maps from degenerating Riemann surfaces