论文标题
曲率维度条件符合Gromov的$ n $ volumic标量曲率
Curvature-Dimension Condition Meets Gromov's $n$-Volumic Scalar Curvature
论文作者
论文摘要
我们研究了本说明中$ n $ volumic标量曲率的属性。 Lott-Sturm-Villani's curvature-dimension condition ${\rm CD}(κ,n)$ was showed to imply Gromov's $n$-volumic scalar curvature $\geq nκ$ under an additional $n$-dimensional condition and we show the stability of $n$-volumic scalar curvature $\geq κ$ with respect to smGH-convergence.然后，我们在加权的riemannian歧管上提出了一种新的加权标态曲率，并显示其特性。
We study the properties of the $n$-volumic scalar curvature in this note. Lott-Sturm-Villani's curvature-dimension condition ${\rm CD}(κ,n)$ was showed to imply Gromov's $n$-volumic scalar curvature $\geq nκ$ under an additional $n$-dimensional condition and we show the stability of $n$-volumic scalar curvature $\geq κ$ with respect to smGH-convergence. Then we propose a new weighted scalar curvature on the weighted Riemannian manifold and show its properties.
