On the equivalence of heat kernel estimates and logarithmic Sobolev inequalities for the Hodge Laplacian

DOI10.1016/J.JDE.2006.10.007zbMath1113.35035OpenAlexW2084341486MaRDI QIDQ863931

Nelia Charalambous

Publication date: 12 February 2007

Published in: Journal of Differential Equations (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.jde.2006.10.007

zbMATH Keywords

heat operatorlogarithmic Sobolev inequalitiesHodge LaplacianultracontractivityBochner techniqueBochner Weitzenböck formula

Mathematics Subject Classification ID

Heat equation (35K05) A priori estimates in context of PDEs (35B45) Partial differential equations on manifolds; differential operators (58J99)

Related Items (3)

Heat flow on 1-forms under lower Ricci bounds. Functional inequalities, spectral theory, and heat kernel ⋮ On the spectrum of the Laplacian ⋮ Spectral gaps on complete Riemannian manifolds

Cites Work

• On the \(L^p\) independence of the spectrum of the Hodge Laplacian on non-compact manifolds
• Analysis of the Laplacian on a complete Riemannian manifold
• Opérateur de courbure et laplacien des formes différentielles d'une variété riemannienne
• Logarithmic Sobolev Inequalities
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