Positive mass theorem and the CR Yamabe equation on 5-dimensional contact spin manifolds

We consider the CR Yamabe equation with critical Sobolev exponent on a closed contact manifold M of dimension 2n+1. The problem of finding solutions with minimum energy has been resolved for all dimensions except for dimension 5 (n=2). In this paper we prove the existence of minimum energy solutions...

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Veröffentlicht in:Advances in mathematics (New York. 1965) 2022-08, Vol.404, p.108446, Article 108446
Hauptverfasser: Cheng, Jih-Hsin, Chiu, Hung-Lin
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Sprache:eng
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Zusammenfassung:We consider the CR Yamabe equation with critical Sobolev exponent on a closed contact manifold M of dimension 2n+1. The problem of finding solutions with minimum energy has been resolved for all dimensions except for dimension 5 (n=2). In this paper we prove the existence of minimum energy solutions in the 5-dimensional case when M is spin. The proof is based on a positive mass theorem built up through a spinorial approach.
ISSN:0001-8708
1090-2082
DOI:10.1016/j.aim.2022.108446