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arXiv · 1408.6872

Curvature-dimension inequalities on sub-Riemannian manifolds obtained from Riemannian foliations, Part II

Erlend Grong·Anton Thalmaier
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Abstract

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 $P_t$ corresponding to the sub-Laplacian. We give bounds for the gradient, entropy, a Poincar\'e inequality and a Li-Yau type inequality. These results require that the gradient of $P_t f$ remains uniformly bounded whenever the gradient of $f$ is bounded and we give several sufficient conditions for this to hold.

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Erlend Grong, Anton Thalmaier. 2014-08-28. Curvature-dimension inequalities on sub-Riemannian manifolds obtained from Riemannian foliations, Part II. https://arxiv.org/abs/1408.6872

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