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arXiv · 1909.00909

Scalar Curvature Volume Comparison Theorems for Almost Rigid Sphere

Yiyue Zhang
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Abstract

Bray's football theorem (\cite{bray2009penrose}) is a weakening of Bishop theorem in dimension 3. It gives a sharp volume upper bound for a three dimensional manifold with scalar curvature larger than $n(n-1)$ and Ricci curvature larger than $\varepsilon$. This paper extends Bray's football theorem in high dimensions, assuming the manifold is axis symmetric or the Ricci curvature has an upper bound.

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Yiyue Zhang. 2019-09-03. Scalar Curvature Volume Comparison Theorems for Almost Rigid Sphere. https://arxiv.org/abs/1909.00909

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