Abstract
Gromov proved a cube inequality on the bound of distances between opposite faces of a cube equipped with a positive scalar curvature metric in dimension $\leq 8$ using a minimal surface method. He conjectured that the cube inequality also holds in dimension $\geq 9$. In this paper, we prove Gromov’s cube inequality in all dimensions with the optimal constant via a Dirac operator method.
Funding Statement
The first-named author is partially supported by NSFC11420101001.
The second-named author is partially supported by NSF 1800737 and 1952693.
The third-named author is partially supported by NSF 1700021, 2000082, 2247313, and the Simons Fellows Program.
Citation
Jinmin Wang. Zhizhang Xie. Guoliang Yu. "A proof of Gromov's cube inequality on scalar curvature." J. Differential Geom. 128 (3) 1285 - 1300, November 2024. https://doi.org/10.4310/jdg/1729092460
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