Asymptotic estimates on the time derivative of \(\Phi\)-entropy on Riemannian manifolds

DOI10.1007/s10114-014-2720-8zbMath1304.60085arXiv1104.3204OpenAlexW2135999072WikidataQ115385223 ScholiaQ115385223MaRDI QIDQ2452407

Bin Qian

Publication date: 3 June 2014

Published in: Acta Mathematica Sinica. English Series (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1104.3204

zbMATH Keywords

curvaturehyperbolic spaceheat kernel\(\Phi\)-entropy

Mathematics Subject Classification ID

Diffusion processes (60J60) Elliptic equations on manifolds, general theory (58J05) Transition functions, generators and resolvents (60J35)

Related Items (1)

A characterization of the rate of change of Ф-entropy via an integral form curvature-dimension condition

Cites Work

• Positive curvature property for sub-Laplacian on nilpotent Lie group of rank two
• A generalization of Hamilton's gradient estimate
• Perelman's entropy formula for the Witten Laplacian on Riemannian manifolds via Bakry-Emery Ricci curvature
• Positive curvature property for some hypoelliptic heat kernels
• Gradient estimates for the heat kernels in higher dimensional Heisenberg groups
• Perelman's entropy and doubling property on Riemannian manifolds
• On gradient bounds for the heat kernel on the Heisenberg group
• The entropy formula for linar heat equation
• Estimation optimale du gradient du semi-groupe de la chaleur sur le groupe de Heisenberg
• Refined convex Sobolev inequalities
• Entropies, convexity, and functional inequalities: on \(\Phi\)-entropies and \(\Phi\)-Sobolev inequalities
• Asymptotic estimates on the time derivative of entropy on a Riemannian manifold
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