Lower bounds of Lipschitz constants on foliations

In this paper we consider Llarull’s theorem in the foliation case and get a lower bound of the Lipschitz constant of the map M→Sn\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$M\rightarrow S^n$$\end{document} in the foliation case under the spin condition.