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arXiv · 2608.20215

On the proof of Bray's conjecture

Xumin Jiang·Mingxiang Li·Zhehui Wang
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Abstract

Let $(M^n,g)$ be a connected, closed, smooth Riemannian manifold with dimension $n\geq 3$. There exists a positive constant $\varepsilon_n<1$ such that, if Ricci curvature $\operatorname{Ric}_g\geq \varepsilon_n(n-1)g$ and the scalar curvature $R_g\geq n(n-1)$, then the volume $V_g(M^n)$ is less than or equal to the volume of standard $n$-sphere. This confirms a conjecture by Bray in 1997.

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Xumin Jiang, Mingxiang Li, Zhehui Wang. 2026-08-20. On the proof of Bray's conjecture. https://arxiv.org/abs/2608.20215

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