Curvature-Dimension Condition Meets Gromov's -Volumic Scalar Curvature - Deng, Jialong (Symmetry, Integrability and Geometry: Methods and Applications, 2021)
We study the properties of the n-volumic scalar curvature in this note. Lott-Sturm-Villani's curvature-dimension condition CD(κ, ) was shown to imply Gromov's -volumic scalar curvature ≥ κ under an additional -dimensional condition, and we show the stability of -volumic scalar curvature ≥ κ with respect to smGH-convergence. Then we propose a new weighted scalar curvature on the weighted Riemannian manifold and show its properties.