Curvature-dimension inequalities on sub-Riemannian manifolds obtained from Riemannian foliations: part II

被引：17

作者：

Grong, Erlend ^{[1
]}

Thalmaier, Anton ^{[1
]}

机构：

[1] Univ Luxembourg, Math Res Unit, FSTC, 6 Rue Richard Coudenhove Kalergi, L-1359 Luxembourg, Luxembourg

来源：

MATHEMATISCHE ZEITSCHRIFT | 2016年 / 282卷 / 1-2期

关键词：

Curvature-dimension inequality; Sub-Riemannian geometry; Hypoelliptic operator; Spectral gap; Riemannian foliations; HEAT KERNEL;

D O I：

10.1007/s00209-015-1535-3

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

Using the curvature-dimension inequality proved in Part I, we look at consequences of this inequality in terms of the interaction between the sub-Riemannian geometry and the heat semigroup corresponding to the sub-Laplacian. We give bounds for the gradient, entropy, a Poincar, inequality and a Li-Yau type inequality. These results require that the gradient of remains uniformly bounded whenever the gradient of f is bounded and we give several sufficient conditions for this to hold.

引用

页码：131 / 164

页数：34

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