@inbook{5ddcd29926ad4cdea4778cd723867a12,
title = "Geometric Inequalities on Riemannian and Sub-Riemannian Manifolds by Heat Semigroups Techniques",
abstract = "In those lecture notes, we review some of the theory of diffusion operators and applications of heat semigroups methods in Riemannian geometry. In particular we will show how Ricci lower bounds and Bochner{\textquoteright}s formula lead to the notion of curvature dimension-equality for the Laplace-Beltrami operator and how this inequality only can be used to prove geometric and functional inequalities such as Li-Yau, Sobolev or isoperimetric inequalities. Some generalizations to sub-Riemannian geometry are given at the end.",
author = "Fabrice Baudoin",
note = "Publisher Copyright: {\textcopyright} 2022, The Author(s), under exclusive license to Springer Nature Switzerland AG.",
year = "2022",
doi = "10.1007/978-3-030-84141-6_2",
language = "English",
series = "Lecture Notes in Mathematics",
publisher = "Springer Science and Business Media Deutschland GmbH",
pages = "7--91",
booktitle = "Lecture Notes in Mathematics",
address = "Germany",
}