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We have decided to discontinue the publication of preprints on our preprint server as of 1 March 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.

MiS Preprint
37/2018

Asymptotic analysis for Dirac-harmonic maps from degenerating spin surfaces and with bounded index

Jürgen Jost, Lei Liu and Miaomiao Zhu

Abstract

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:
May 23, 2018
Published:
May 24, 2018
MSC Codes:
53C43, 58E20
Keywords:
Dirac-harmonic maps, degenerating spin surface, blow-up, neck analysis, index, Pohozaev type constant

Related publications

inJournal
2019 Journal Open Access
Jürgen Jost, Lei Liu and Miaomiao Zhu

Asymptotic analysis for Dirac-harmonic maps from degenerating spin surfaces and with bounded index

In: Calculus of variations and partial differential equations, 58 (2019) 4, p. 142