Generalized $S^1$-stability theorem

Tongrui Wang; Xuan Yao

Generalized $S^1$-stability theorem

Differential Geometry 2023-09-26 v1 Geometric Topology

Authors: Tongrui Wang , Xuan Yao

Abstract

We use the equivariant $\mu$ -bubbles technique to prove that for any compact manifold $M^n$ with non-empty boundary, $n\in\{3,5,6\}$ , the Yamabe invariant of $M^n$ is positive if and only if the Yamabe invariant of $M^n\times S^1$ is positive. This generalized the $S^1$ -stability conjecture of Rosenberg to compact manifolds with boundary.

Keywords

yamabe problem riemannian geometry stability theory

Cite

@article{arxiv.2309.13865,
  title  = {Generalized $S^1$-stability theorem},
  author = {Tongrui Wang and Xuan Yao},
  journal= {arXiv preprint arXiv:2309.13865},
  year   = {2023}
}

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