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Positive mass theorem and the CR Yamabe equation on 5-dimensional contact spin manifolds (2107.04209v1)
Published 9 Jul 2021 in math.DG and math.CV
Abstract: 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 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.