The subelliptic heat kernels on \(\mathbf{SL}(2,\mathbb{R})\) and on its universal covering \(\widetilde{\mathbf{SL}(2,\mathbb{R})}\): Integral representations and some functional inequalities

DOI10.1007/s11118-011-9230-4zbMath1236.43006arXiv0906.1977OpenAlexW2589454718MaRDI QIDQ663501

Michel Bonnefont

Publication date: 15 February 2012

Published in: Potential Analysis (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/0906.1977

zbMATH Keywords

heat kernelfunctional inequalitiessubelliptic geometry

Mathematics Subject Classification ID

Analysis on other specific Lie groups (43A80) Heat and other parabolic equation methods for PDEs on manifolds (58J35) Subelliptic equations (35H20)

Related Items (13)

The subelliptic heat kernel on the anti-de Sitter space ⋮ The subelliptic heat kernel on the CR sphere ⋮ Stochastic areas, winding numbers and Hopf fibrations ⋮ Small-time asymptotics for subelliptic Hermite functions on \(SU(2)\) and the CR sphere ⋮ Couplings of Brownian motions on \(\mathrm{SU}(2,\mathbb{C})\) ⋮ Decompositions of Diffusion Operators and Related Couplings ⋮ The subelliptic heat kernels of the quaternionic Hopf fibration ⋮ Integral representation of the sub-elliptic heat kernel on the complex anti-de Sitter fibration ⋮ Hamilton type gradient estimate for the sub-elliptic operators ⋮ Revisiting the heat kernel on isotropic and nonisotropic Heisenberg groups* ⋮ Heat content and horizontal mean curvature on the Heisenberg group ⋮ The horizontal heat kernel on the quaternionic anti-de Sitter spaces and related twistor spaces ⋮ Log-Sobolev inequalities for subelliptic operators satisfying a generalized curvature dimension inequality

Cites Work

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• On Carnot-Caratheodory metrics
• A logarithmic Sobolev form of the Li-Yau parabolic inequality
• On gradient bounds for the heat kernel on the Heisenberg group
• The subelliptic heat kernel on \(\mathbf{SU}(2)\): representations, asymptotics and gradient bounds
• Majoration en temps petit de la densité d'une diffusion dégénérée
• Minoration en temps petit de la densité d'une diffusion dégénérée. (Lower estimate for small times of the density of a degenerate diffusion)
• Asymptotics for some Green kernels on the Heisenberg group and the Martin boundary
• Least action principle, heat propagation and subelliptic estimates on certain nilpotent groups
• Small-time Gaussian behavior of symmetric diffusion semigroups
• Hamilton-Jacobi theory and the heat kernel on Heisenberg groups
• Hypoelliptic heat kernel inequalities on the Heisenberg group
• Partial differential equations. 2: Qualitative studies of linear equations
• Differential geometry and analysis on CR manifolds
• Estimation optimale du gradient du semi-groupe de la chaleur sur le groupe de Heisenberg
• Isoperimetric inequalities & volume comparison theorems on CR manifolds
• Théorème central limite local sur certains groupes de Lie
• The distribution of energy in the Brownian motion in the Gaussian field and analytic-hypoellipticity of certain subelliptic operators on the Heisenberg group
• [https://portal.mardi4nfdi.de/wiki/Publication:5689214 Isoperimetric and Sobolev inequalities for Carnot-Carath�odory spaces and the existence of minimal surfaces]

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