Lower bounds of Lipschitz constants on foliations

TL;DR

This paper extends Llarull's theorem to foliated manifolds, establishing lower bounds on Lipschitz constants for maps to spheres under spin conditions, advancing geometric analysis in foliated contexts.

Contribution

It generalizes Llarull's theorem to foliations with spin conditions, providing new lower bounds on Lipschitz constants for maps to spheres.

Findings

Established lower bounds for Lipschitz constants in foliated manifolds.

Extended geometric inequalities to the setting of foliations.

Provided conditions under which the bounds hold.

Abstract

In this paper we consider Llarull's theorem in the foliation case and get a lower bound of the Lipschitz constant of the map $M\to S^n$ in the foliation case under the spin condition.