MiS Preprint Repository
We have decided to discontinue the publication of preprints on our preprint server end of 2024. The publication culture within mathematics has changed so much due to the rise of repositories such as ArXiV (www.arxiv.org) that we are encouraging all institute members to make their preprints available there. An institute's repository in its previous form is, therefore, unnecessary. The preprints published to date will remain available here, but we will not add any new preprints here.
Asymptotic analysis for Dirac-harmonic maps from degenerating spin surfaces and with bounded index
Jürgen Jost, Lei Liu and Miaomiao ZhuAbstract
We study the refined blow-up behaviour of a sequence of Dirac-harmonic maps from degenerating spin surfaces with uniformly bounded energy in the case that the domain surfaces converge to a spin surface with only Neveu-Schwarz type nodes. For Dirac-harmonic necks appearing near the nodes, we show that the limit of the map part of each neck is a geodesic in the target manifold. Moreover, we give a length formula for the limit geodesics appearing near the node in terms of the Pohozaev type constants associated to the sequence. In particular, if the Ricci curvature of the target manifold has a positive lower bound and the Dirac-harmonic sequence has bounded index, then the limit of the map part of the necks consist of geodesics of finite length and the energy identities hold.
- Received:
- 23.05.18
- Published:
- 24.05.18
- MSC Codes:
- 53C43, 58E20
- Keywords:
- Dirac-harmonic maps, degenerating spin surface, blow-up, neck analysis, index, Pohozaev type constant