Year: 2024
Type: article
Abstract: : In this note, we study the Gehring link problem in the round sphere, which motivates our study of the width of a band in positively curved manifolds. Using the same idea, we are able to prove a sphere theorem for hypersurface in the round $\SS^n$ provided that its normal injectivity radius is large. A rigidity theorem for Clifford hypersurfaces in $\SS^n$ is also proved. The $3$-dimensional case of our theorems confirm two conjectures raised by Gromov (2018).
Source: American Journal of Mathematics
Author: Jian Ge
Language: English
Subfield: Applied Mathematics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W4402873781