108 citations · 389 across the 75 of their papers we have counts for
24 papers · 1 filter
Variations of the sub-Riemannian distance on Sasakian manifolds with applications to coupling
Fabrice Baudoin, Erlend Grong, Robert Neel +1
On Sasakian manifolds with their naturally occurring sub-Riemannian structure, we consider parallel and mirror maps along geodesics of a taming Riemannian metric. We show that thes…
A horizontal Chern-Gauss-Bonnet formula on totally geodesic foliations
Fabrice Baudoin, Erlend Grong, Gianmarco Vega-Molino
Under suitable conditions, we show that the Euler characteristic of a foliated Riemannian manifold can be computed only from curvature invariants which are transverse to the leaves…
Brownian motions and heat kernel lower bounds on Kähler and quaternion Kähler manifolds
Fabrice Baudoin, Guang Yang
We study the radial parts of the Brownian motions on Kähler and quaternion Kähler manifolds. Thanks to sharp Laplacian comparison theorems, we deduce as a consequence a sharp Cheeg…
The Subelliptic Heat Kernel of the Octonionic Anti-De Sitter Fibration
Fabrice Baudoin, Gunhee Cho
In this note, we study the sub-Laplacian of the 15-dimensional octonionic anti-de Sitter space which is obtained by lifting with respect to the anti-de Sitter fibration the Laplaci…
Comparison theorems on H-type sub-Riemannian manifolds
Fabrice Baudoin, Erlend Grong, Luca Rizzi +1
On H-type sub-Riemannian manifolds we establish sub-Hessian and sub-Laplacian comparison theorems which are uniform for a family of approximating Riemannian metrics converging to t…
Improved Beckner-Sobolev inequalities on Kähler manifolds
Fabrice Baudoin, Ovidiu Munteanu
We prove new Beckner-Sobolev type inequalities on compact Kähler manifolds with positive Ricci curvature. As an application, we obtain a diameter upper bound that improves the Bonn…
The subelliptic heat kernel of the octonionic Hopf fibration
Fabrice Baudoin, Gunhee Cho
We study the sub-Laplacian of the -dimensional unit sphere which is obtained by lifting with respect to the Hopf fibration the Laplacian of the octonionic projective space. We…
H-type foliations
Fabrice Baudoin, Erlend Grong, Gianmarco Vega-Molino +1
With a view toward sub-Riemannian geometry, we introduce and study H-type foliations. These structures are natural generalizations of K-contact geometries which encompass as specia…
The horizontal heat kernel on the quaternionic anti de-Sitter spaces and related twistor spaces
Fabrice Baudoin, Nizar Demni, Jing Wang
The geometry of the quaternionic anti-de Sitter fibration is studied in details. As a consequence, we obtain formulas for the horizontal Laplacian and subelliptic heat kernel of th…
Transverse Weitzenböck formulas and de Rham cohomology of totally geodesic foliations
Fabrice Baudoin, Erlend Grong
We prove transverse Weitzenböck identities for the horizontal Laplacians of a totally geodesic foliation. As a consequence, we obtain nullity theorems for the de Rham cohomology as…
Sub-Laplacian comparison theorems on totally geodesic Riemannian foliations
Fabrice Baudoin, Erlend Grong, Kazumasa Kuwada +1
We develop a variational theory of geodesics for the canonical variation of the metric of a totally geodesic foliation. As a consequence, we obtain comparison theorems for the hori…
Curvature-dimension estimates for the Laplace-Beltrami operator of a totally geodesic foliation
Fabrice Baudoin, Michel Bonnefont
We study Bakry-Emery type estimates for the Laplace-Beltrami operator of a totally geodesic foliation. In particular, we are interested in situations for which the operator m…
Sub-Laplacians and hypoelliptic operators on totally geodesic Riemannian foliations
Fabrice Baudoin
These notes are the basis of a course given at the Institut Henri Poincare in September 2014. We survey some recent results related to the geometric analysis of hypoelliptic diffus…
Transverse Weitzenböck formulas and curvature dimension inequalities on Riemannian foliations with totally geodesic leaves
Fabrice Baudoin, Bumsik Kim, Jing Wang
We prove a family of new Weitzenböck formulas on a Riemannian foliation with totally geodesic leaves. These Weitzenböck formulas are naturally parametrized by the canonical variati…
The Lichnerowicz-Obata theorem on sub-Riemannian manifolds with transverse symmetries
Fabrice Baudoin, Bumsik Kim
We prove a lower bound for the first eigenvalue of the sub-Laplacian on sub-Riemannian manifolds with transverse symmetries. When the manifold is of H-type, we obtain a correspondi…
The subelliptic heat kernel on the three dimensional solvable Lie groups
Fabrice Baudoin, Matthew Cecil
We study the subelliptic heat kernels of the CR three dimensional solvable Lie groups. We first classify all left-invariant sub-Riemannian structures on three dimensional solvable…
Curvature dimension inequalities and subelliptic heat kernel gradient bounds on contact manifolds
Fabrice Baudoin, Jing Wang
We study curvature dimension inequalities for the sub-Laplacian on contact Riemannian manifolds. This new curvature dimension condition is then used to obtain: 1) Geometric conditi…
Volume and distance comparison theorems for sub-Riemannian manifolds
Fabrice Baudoin, Michel Bonnefont, Nicola Garofalo +1
In this paper we study global distance estimates and uniform local volume estimates in a large class of sub-Riemannian manifolds. Our main device is the generalized curvature dimen…
Sub-Riemannian balls in CR Sasakian manifolds
Fabrice Baudoin, Michel Bonnefont
We prove global estimates for the sub-Riemannian distance of CR Sasakian manifolds with non negative horizontal Webster-Tanaka Ricci curvature. In particular, in this setting, larg…
Curvature-dimension inequalities and Ricci lower bounds for sub-Riemannian manifolds with transverse symmetries
Fabrice Baudoin, Nicola Garofalo
Let $\M$ be a smooth connected manifold endowed with a smooth measure and a smooth locally subelliptic diffusion operator satisfying , and which is symmetric with res…
A note on lower bounds estimates for the Neumann eigenvalues of manifolds with positive Ricci curvature
Fabrice Baudoin, Alice Vatamanelu
We study new heat kernel estimates for the Neumann heat kernel on a compact manifold with positive Ricci curvature and convex boundary. As a consequence, we obtain new lower bounds…
A sub-Riemannian curvature-dimension inequality, volume doubling property and the Poincaré inequality
Fabrice Baudoin, Michel Bonnefont, Nicola Garofalo
Let be a smooth connected manifold endowed with a smooth measure and a smooth locally subelliptic diffusion operator satisfying , and which is symmetric…
Perelman's entropy and doubling property on Riemannian manifolds
Fabrice Baudoin, Nicola Garofalo
The purpose of this work is to study some monotone functionals of the heat kernel on a complete Riemannian manifold with nonnegative Ricci curvature. In particular, we show that on…
Generalized Bochner formulas and Ricci lower bounds for sub-Riemannian manifolds of rank two
Fabrice Baudoin, Nicola Garofalo
We study a new class of rank two sub-Riemannian manifolds encompassing Riemannian manifolds, CR manifolds with vanishing Webster-Tanaka torsion, orthonormal bundles over Riemannian…