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

TL;DR

This paper proves the existence of minimum energy solutions to the CR Yamabe equation on 5-dimensional contact spin manifolds, using a positive mass theorem and spinorial methods, filling a gap in the understanding of this problem.

Contribution

It establishes the existence of solutions in the 5-dimensional case, which was previously unresolved, by developing a positive mass theorem via spinorial techniques.

Findings

Existence of minimum energy solutions in 5D contact spin manifolds.

Development of a positive mass theorem using spinorial approach.

Extension of solutions to the CR Yamabe problem in dimension 5.

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.