A weighted Llarull type theorem and its applications
Abstract
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. As an application, we establish two Llarull type theorems in the forms of S k × T n − k \mathbb {S}^k\times \mathbb {T}^{n-k} and S k × R n − k \mathbb {S}^k \times \mathbb {R}^{n-k} , respectively.
Fields of Study & Subjects
Geometric Analysis and Curvature Flows
Nonlinear Partial Differential Equations
Advanced Operator Algebra Research
Publication details
- Journal / source
- Proceedings of the American Mathematical Society
- Volume
- 154
- Issue
- 10
- Pages
- 4453–4467
- Publication date
- 24 April 2026
- Language
- EN