Mathematische Annalen

, Volume 355, Issue 4, pp 1255–1299 | Cite as

A perturbation method for spinorial Yamabe type equations on \(S^m\) and its application

  • Takeshi IsobeEmail author


For \(m\ge 2\), we prove the existence of non-trivial solutions for a certain kind of nonlinear Dirac equations with critical Sobolev nonlinearities on \(S^m\) via a perturbative variational method. For the special case \(m=2\), this establishes the existence of a conformal immersion \(S^2\rightarrow \mathbb R ^3\) with prescribed mean curvature \(H\) which is close to a positive constant under an index counting condition on \(H\).

Mathematics Subject Classification (2000)

35Q41 53C42 57R70 58E05 



I would like to express my gratitude to the anonymous referee for drawing my attention to the four vertex theorem and the recent result of M. Anderson [11]. He also gave me a lot of helpful suggestions that made this paper much easier to read.


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© Springer-Verlag 2012

Authors and Affiliations

  1. 1.Department of Mathematics, Graduate School of Science and EngineeringTokyo Institute of TechnologyTokyoJapan

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