A note on a Bonnet-Myers type diameter bound for graphs with positive entropic Ricci curvature

Curvature dimension inequalities and subelliptic heat kernel gradient bounds on contact manifolds

We study curvature dimension inequalities for the sub-Laplacian on contact Riemannian manifolds. This new curvature dimension condition is then used to obtain: 1) Geometric conditions ensuring the compactness of the underlying manifold (Bonnet-Myers type results); 2) Volume estimates of metric balls; 3) Gradient bounds and stochastic completeness for the heat semigroup generated by the sub-Laplacian; 4) Spectral gap estimates.

Lagrangian calculus for nonsymmetric diffusion operators

We characterize lower bounds for the Bakry-Emery Ricci tensor of nonsymmetric diffusion operators by convexity of entropy on the $L^2$-Wasserstein space, and define a curvature-dimension condition for general metric measure spaces together with a square integrable $1$-form in the sense of \cite{giglinonsmooth}. This extends the Lott-Sturm-Villani approach for lower Ricci curvature bounds of metric measure spaces. In generalized smooth context, consequences are new Bishop-Gromov estimates, pre-compactness under measured Gromov-Hausdorff convergence, and a Bonnet-Myers theorem that generalizes p…

基于最优输运的低正则性时空的类时Ricci界

Timelike Ricci bounds for low regularity spacetimes by optimal transport

该研究针对低正则性时空，利用最优输运方法证明了分布意义下类时Ricci有下界的C¹正则整体双曲时空满足类时测度收缩性质及相关几何不等式，C¹,¹正则下还成立更强曲率-维数条件且耦合与测地线唯一。