Generalized $S^1$-stability theorem

Tongrui Wang; Xuan Yao

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arXiv · 2309.13865

Generalized $S^1$-stability theorem

Tongrui Wang·Xuan Yao

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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.

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Tongrui Wang, Xuan Yao. 2023-09-25. Generalized $S^1$-stability theorem. https://arxiv.org/abs/2309.13865

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