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arXiv · 2112.04594

Macroscopic scalar curvature and codimension 2 width

Hannah Alpert·Alexey Balitskiy·Larry Guth
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Abstract

We show that a complete $3$-dimensional Riemannian manifold $M$ with finitely generated first homology has macroscopic dimension $1$ if it satisfies the following "macroscopic curvature" assumptions: every ball of radius $10$ in $M$ has volume at most $4$, and every loop in every ball of radius $1$ in $M$ is null-homologous in the concentric ball of radius $2$.

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Hannah Alpert, Alexey Balitskiy, Larry Guth. 2021-12-08. Macroscopic scalar curvature and codimension 2 width. https://doi.org/10.1142/s1793525323500024

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