  In this note, we study the Gehring link problem in the round sphere, which
motives our study of the width of a band in positively curved manifolds. Using
the same idea, we are able to get a sphere theorem for hypersurface in in the
round $S^{n}$ in terms of its focal radius as well as the rigidity of Clifford
hypersurface in $S^{n}$. The $3$-dimension case of our theorems confirm two
conjectures raised by Gromov in [Gro18].
