论文标题
通过广义伽马$ z $微积分，亚riemannian ricci曲率
Sub-Riemannian Ricci curvature via generalized Gamma $z$ calculus
论文作者
论文摘要
我们为亚riemannian歧管提供了亚riemannian ricci曲率张量。我们提供了包括任意加权体积的Heisenberg组，位移组和Martinet次摩曼尼亚结构，其中包括亚riemannian曲率维度界限和log-sobolev不等式的分析范围。 {These bounds can be used to establish the entropy dissipation results for sub-Riemannian drift diffusion processes on a compact spatial domain, in term of $L_1$ distance.} Our derivation of Ricci curvature is based on generalized Gamma $z$ calculus and $z$--Bochner's formula, where $z$ stands for extra directions introduced into the sub-Riemannian degenerate structure.
We derive sub-Riemannian Ricci curvature tensor for sub-Riemannian manifolds. We provide examples including the Heisenberg group, displacement group, and Martinet sub-Riemannian structure with arbitrary weighted volumes, in which we establish analytical bounds for sub-Riemannian curvature dimension bounds and log-Sobolev inequalities. {These bounds can be used to establish the entropy dissipation results for sub-Riemannian drift diffusion processes on a compact spatial domain, in term of $L_1$ distance.} Our derivation of Ricci curvature is based on generalized Gamma $z$ calculus and $z$--Bochner's formula, where $z$ stands for extra directions introduced into the sub-Riemannian degenerate structure.
