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

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

2008-03-26

arxiv.org/abs/0803.3723v1

Calc. Var. Partial Differential Equations 35 (2009), no. 2, 169-189

Mathematics

Differential Geometry

24 pages

Scientific paper

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.

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