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Asymptotic mean value Laplacian on equiregular sub-Riemannian manifolds
Fabrice Baudoin, Jonathan Junné, David Tewodrose
Let be a smooth equiregular sub-Riemannian manifold equipped with a smooth positive measure . We study the small-scale limit of the metric-ball mean-value op…
Sub-Riemannian Selberg Trace Formulae for Compact Quotients of SL(2,R) and Determinants of Sub-Laplacians
Fabrice Baudoin
We prove sub-Riemannian Selberg trace formulae for compact quotients of SL(2,R). Using the Fourier decomposition along the SO(2)-fibers, we reduce the heat trace computation to the…
Sub-Laplacian comparison theorems on Riemannian foliations with minimal leaves and applications
Fabrice Baudoin
We prove comparison theorems for the horizontal Laplacian of the Riemannian distance in the context of Riemannian foliations with minimal leaves. This general framework generalizes…
Topology and bottom spectrum of transversally negatively curved foliations
Fabrice Baudoin
We show that for any Riemannian foliation with a simply connected and negatively curved leaf space the normal exponential map of a leaf is a diffeomorphism. As an application, if t…
Geometric Inequalities on Riemannian and sub-Riemannian manifolds by heat semigroups techniques
Fabrice Baudoin
In those lecture notes, we review some applications of heat semigroups methods in Riemannian and sub-Riemannian geometry. The notes contain parts of courses taught at Purdue Univer…