Curvature-Dimension Condition Meets Gromov's $n$-Volumic Scalar Curvature

Jialong Deng

Symmetry, integrability and geometry: methods and applications, Tome 17 (2021)

Résumé

We study the properties of the $n$-volumic scalar curvature in this note. Lott–Sturm–Villani's curvature-dimension condition ${\rm CD}(\kappa,n)$ was showed to imply Gromov's $n$-volumic scalar curvature $\geq n\kappa$ under an additional $n$-dimensional condition and we show the stability of $n$-volumic scalar curvature $\geq \kappa$ with respect to smGH-convergence. Then we propose a new weighted scalar curvature on the weighted Riemannian manifold and show its properties.

Détail

Keywords: curvature-dimension condition, $n$-volumic scalar curvature, stability, weighted scalar curvature ${\rm Sc}_{\alpha, \beta}$.

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