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Positive mass theorem and the CR Yamabe equation on 5-dimensional contact spin manifolds Cheng, Jih-Hsin


We consider the CR Yamabe equation with critical Sobolev ex-ponent 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. This is joint work with Hung-Lin Chiu.

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