Sobolev, Poincaré, and isoperimetric inequalities for subelliptic diffusion operators satisfying a generalized curvature dimension inequality

DOI10.4171/RMI/771zbMath1287.53026arXiv1203.3789MaRDI QIDQ2449574

Bumsik Kim, Fabrice Baudoin

Publication date: 8 May 2014

Published in: Revista Matemática Iberoamericana (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1203.3789

zbMATH Keywords

isoperimetric inequalityPoincaré inequalitySobolev inequalitiessubelliptic operator

Mathematics Subject Classification ID

Sobolev spaces and other spaces of ``smooth functions, embedding theorems, trace theorems (46E35) Sub-Riemannian geometry (53C17) Subelliptic equations (35H20) Inequalities applied to PDEs involving derivatives, differential and integral operators, or integrals (35A23)

Related Items (11)

Sub-Riemannian curvature of Carnot groups with rank-two distributions ⋮ Besov class via heat semigroup on Dirichlet spaces. II: BV functions and Gaussian heat kernel estimates ⋮ The bounded variation capacity and Sobolev-type inequalities on Dirichlet spaces ⋮ Solution of the qc Yamabe equation on a 3-Sasakian manifold and the quaternionic Heisenberg group ⋮ An Obata type result for the first eigenvalue of the sub-Laplacian on a CR manifold with a divergence-free torsion ⋮ Curvature dimension inequalities and subelliptic heat kernel gradient bounds on contact manifolds ⋮ Besov class via heat semigroup on Dirichlet spaces. III: BV functions and sub-Gaussian heat kernel estimates ⋮ A Lichnerowicz estimate for the spectral gap of a sub-Laplacian ⋮ The Lichnerowicz-Obata theorem on sub-Riemannian manifolds with transverse symmetries ⋮ Generalized Bakry-Émery curvature condition and equivalent entropic inequalities in groups ⋮ Differential Harnack inequalities and Perelman type entropy formulae for subelliptic operators

Cites Work

• Unnamed Item
• Curvature-dimension inequalities and Ricci lower bounds for sub-Riemannian manifolds with transverse symmetries
• Log-Sobolev inequalities for subelliptic operators satisfying a generalized curvature dimension inequality
• An introduction to the Heisenberg group and the sub-Riemannian isoperimetric problem
• A general rearrangement inequality for multiple integrals
• A sub-Riemannian curvature-dimension inequality, volume doubling property and the Poincaré inequality

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