18 citations · 32 across the 4 of their papers we have counts for
4 papers
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…
Poincare inequality and the uniqueness of solutions for the heat equation associated with subelliptic diffusion operators
Bumsik Kim
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.…
Sobolev, Poincare and isoperimetric inequalities for subelliptic diffusion operators satisfying a generalized curvature dimension inequality
Fabrice Baudoin, Bumsik Kim
By adapting some ideas of M. Ledoux \cite{ledoux2}, \cite{ledoux-stflour} and \cite{Led} to a sub-Riemannian framework we study Sobolev, Poincaré and isoperimetric inequalities ass…