Best constants in the L2-Nash inequality

DOI10.1017/S0308210500001025zbMath1040.53048OpenAlexW1967693824MaRDI QIDQ2731105

Emmanuel Humbert

Publication date: 2001

Published in: Proceedings of the Royal Society of Edinburgh: Section A Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1017/s0308210500001025

zbMATH Keywords

compact Riemannian manifoldscomplete manifoldsmanifolds with boundaryNash inequalityCartan-Hadamard conjecture

Mathematics Subject Classification ID

Relations of PDEs with special manifold structures (Riemannian, Finsler, etc.) (58J60) Methods of global Riemannian geometry, including PDE methods; curvature restrictions (53C21) Inequalities involving derivatives and differential and integral operators (26D10)

Related Items (12)

Optimal improved \(L_p\)-Riemannian Gagliardo-Nirenberg inequalities ⋮ On Nash and Carlson's inequalities for symmetric \(q\)-integral transforms ⋮ Optimal normed Sobolev type inequalities on manifolds. I: The Nash prototype ⋮ Sharp Nash inequalities on manifolds with boundary in the presence of symmetries ⋮ On the second best constant in logarithmic Sobolev inequalities on complete Riemannian manifolds. ⋮ Sharp Nash inequalities on the unit sphere: the influence of symmetries ⋮ Extremals for sharp GNS inequalities on compact manifolds ⋮ Sharp constants in Riemannian \(L^p\)-Gagliardo-Nirenberg inequalities ⋮ Optimal \(L^p\)-Riemannian Gagliardo-Nirenberg inequalities ⋮ Extremal functions for the sharp \(L^2\)-Nash inequality ⋮ Extremal maps in Sobolev type inequalities: some remarks ⋮ Sharp \(L^p\)-entropy inequalities on manifolds

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