# Log-Sobolev inequalities for subelliptic operators satisfying a generalized curvature dimension inequality

@article{Baudoin2011LogSobolevIF,
title={Log-Sobolev inequalities for subelliptic operators satisfying a generalized curvature dimension inequality},
author={Fabrice Baudoin and Michel Bonnefont},
journal={arXiv: Functional Analysis},
year={2011}
}
• Published 2 June 2011
• Mathematics
• arXiv: Functional Analysis

### A sub-Riemannian curvature-dimension inequality, volume doubling property and the Poincaré inequality

• Mathematics
• 2010
Let $$\mathbb M$$M be a smooth connected manifold endowed with a smooth measure $$\mu$$μ and a smooth locally subelliptic diffusion operator $$L$$L satisfying $$L1=0$$L1=0, and which is symmetric

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

• Mathematics
• 2016
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 $$P_t$$Pt

### Poincare inequality and the uniqueness of solutions for the heat equation associated with subelliptic diffusion operators

In this paper we study global Poincare inequalities on balls in a large class of sub-Riemannian manifolds satisfying the generalized curvature dimension inequality introduced by F.Baudoin and

### Dimension free Harnack inequalities on $\RCD(K, \infty)$ spaces

The dimension free Harnack inequality for the heat semigroup is established on the $\RCD(K,\infty)$ space, which is a non-smooth metric measure space having the Ricci curvature bounded from below in

### Heat kernel upper bounds under the generalized curvature(-dimension) inequality

In the sub-Riemannian manifolds, on the one hand, following Baudoin-Garofalo \cite{BaudoinGarofalo}, the upper bound for heat kernels associated to a class of locally subelliptic operators are given

### Heat kernel upper bounds under the generalized curvature(-dimension) inequality

In the sub-Riemannian manifolds, on the one hand, following Baudoin-Garofalo [5], the upper bound for heat kernels associated to a class of locally subelliptic operators are given under the

### Sub-Riemannian Ricci curvature via generalized Gamma $z$ calculus

• Mathematics
• 2020
We derive sub-Riemannian Ricci curvature tensor for sub-Riemannian manifolds. We provide examples including the Heisenberg group, displacement group ($\textbf{SE}(2)$), and Martinet sub-Riemannian

### Curvature Dimension Inequalities and Subelliptic Heat Kernel Gradient Bounds on Contact Manifolds

• Mathematics
Potential Analysis
• 2013
AbstractWe study curvature dimension inequalities for the sub-Laplacian on contact Riemannian manifolds. This new curvature dimension condition is then used to obtain: Geometric conditions ensuring

### Generalized Curvature Condition for Subelliptic Diffusion Processes

By using a general version of curvature condition, derivative inequalities are established for a large class of subelliptic diffusion semigroups. As applications, the

## References

SHOWING 1-10 OF 54 REFERENCES

### A sub-Riemannian curvature-dimension inequality, volume doubling property and the Poincaré inequality

• Mathematics
• 2010
Let $$\mathbb M$$M be a smooth connected manifold endowed with a smooth measure $$\mu$$μ and a smooth locally subelliptic diffusion operator $$L$$L satisfying $$L1=0$$L1=0, and which is symmetric

### Logarithmic Sobolev inequalities on noncompact Riemannian manifolds

Summary. This paper presents a dimension-free Harnack type inequality for heat semigroups on manifolds, from which a dimension-free lower bound is obtained for the logarithmic Sobolev constant on

### Curvature-dimension inequalities and Ricci lower bounds for sub-Riemannian manifolds with transverse symmetries

• Mathematics
• 2011
Let $\M$ be a smooth connected manifold endowed with a smooth measure $\mu$ and a smooth locally subelliptic diffusion operator $L$ satisfying $L1=0$, and which is symmetric with respect to $\mu$.

### Nash and log-Sobolev inequalities for hypoelliptic operators

By estimating the intrinsic distance and using known heat kernel upper bounds, the global Nash inequality with exact dimension is established for a class of square fields with algebraic growth

### Logarithmic Sobolev Inequalities for Infinite Dimensional Hörmander Type Generators on the Heisenberg Group

• Mathematics
• 2009
The Heisenberg group is one of the simplest sub-Riemannian settings in which we can define non-elliptic Hörmander type generators. We can then consider coercive inequalities associated to such

### ISOPERIMETRIC AND SOBOLEV INEQUALITIES FOR CARNOT-CARATHEODORY SPACES AND THE EXISTENCE OF MINIMAL SURFACES

• Mathematics
• 1996
After Hormander's fundamental paper on hypoellipticity [54], the study of partial differential equations arising from families of noncommuting vector fields has developed significantly. In this paper

### Generalization of an Inequality by Talagrand and Links with the Logarithmic Sobolev Inequality

• Mathematics
• 2000
Abstract We show that transport inequalities, similar to the one derived by M. Talagrand (1996, Geom. Funct. Anal. 6 , 587–600) for the Gaussian measure, are implied by logarithmic Sobolev

### Quasi-invariance for heat kernel measures on sub-Riemannian infinite-dimensional Heisenberg groups

• Mathematics
• 2011
We study heat kernel measures on sub-Riemannian infinite- dimensional Heisenberg-like Lie groups. In particular, we show that Cameron-Martin type quasi-invariance results hold in this subelliptic

### Geometric Inequalities and Generalized Ricci Bounds in the Heisenberg Group

We prove that no curvature-dimension bound CD(K,N) holds in any Heisenberg group . On the contrary, the measure contraction property MCP(0, 2n + 3) holds and is optimal for the dimension 2n + 3. For