Jintian Zhu
Published 2020-03-03Version 1
In this short note, we use the $\mu$-bubble method to prove a width estimate for overtorical bands with positive sectional curvatures in dimensions between 3 and 7, which reveals a quantitive difference between positive scalar curvature and positive sectional curvature. This verifies a conjecture of Gromov in [2] when the dimension is 3. As a corollary, we obtain a characterization of the Clifford torus with focal radius.
Positive scalar curvature on spin pseudomanifolds: the fundamental group and secondary invariants
Positive scalar curvature on stratified spaces, I: the simply connected case
Rigidity of Area-Minimizing $2$-Spheres in $n$-Manifolds with Positive Scalar Curvature
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