A Weighted Llarull Type Theorem and its applications

This paper generalizes Llarull’s classical scalar curvature rigidity theorem to the setting of weighted manifolds with P-scalar curvature. More precisely, we prove the refinement of Llarull’s theorem for P-scalar curvature, which is similar to Listing’s work \cite{listing2010scalar}. As an application, we establish a Llarull type theorem in the form of ${\mathbb{S}}^k\times {\mathbb{T}}^{n-k}$.