Llarull's theorem on punctured sphere with L^∞ metric

The classical Llarull theorem states that a smooth metric on n-sphere cannot have scalar curvature no less than n(n-1) and dominate the standard spherical metric at the same time unless it is the standard spherical metric. In this work, we prove that Llarull's rigidity theorem holds for L^∞ metrics on spheres with finitely many points punctured. This is related to a question of Gromov.