Sobolev inequalities on forms and \(L^{p,q}\)-cohomology on complete Riemannian manifolds

DOI10.1007/s12220-009-9114-7zbMath1192.46031OpenAlexW2014232655WikidataQ115376914 ScholiaQ115376914MaRDI QIDQ848507

Xiang Dong Li

Publication date: 3 March 2010

Published in: The Journal of Geometric Analysis (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s12220-009-9114-7

zbMATH Keywords

Bakry-Emery Ricci curvature\(L^{p, q}\)-cohomologyCartan-de Rham equationHodge systemsSobolev inequalities on forms Weitzenböck curvature

Mathematics Subject Classification ID

Sobolev spaces and other spaces of ``smooth functions, embedding theorems, trace theorems (46E35) de Rham theory in global analysis (58A12) Hodge theory in global analysis (58A14) Partial differential equations on manifolds; differential operators (58J99) Methods of global Riemannian geometry, including PDE methods; curvature restrictions (53C21)

Related Items

On the \(L^{r}\) Hodge theory in complete non compact Riemannian manifolds ⋮ The Hölder-Poincaré duality for \(L _{q,p }\)-cohomology ⋮ Riesz transforms on forms and \(L^p\)-Hodge decomposition on complete Riemannian manifolds ⋮ Harmonic 1-forms on immersed hypersurfaces in a Riemannian manifold with weighted bi-Ricci curvature bounded from below ⋮ Hamilton's Harnack inequality and the \(W\)-entropy formula on complete Riemannian manifolds ⋮ On the strong \(L^p\)-Hodge decomposition over complete Riemannian manifolds

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