Year: 2024
Type: article
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.
Source: Journal of Differential Geometry
Authors: Jinmin Wang, Zhizhang Xie, Guoliang Yu
Institutions: Chinese Academy of Sciences, Texas A&M University
Language: English
Subfield: Applied Mathematics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W4403451901