Sharp Sobolev inequalities on noncompact Riemannian manifolds with \(\mathrm{Ric} \geq 0\) via optimal transport theory
From MaRDI portal
Publication:6597637
DOI10.1007/s00526-024-02810-9MaRDI QIDQ6597637
Publication date: 3 September 2024
Published in: Calculus of Variations and Partial Differential Equations (Search for Journal in Brave)
Sobolev spaces and other spaces of ``smooth functions, embedding theorems, trace theorems (46E35) Integration with respect to measures and other set functions (28A25) Inequalities for sums, series and integrals (26D15) Relations of PDEs with special manifold structures (Riemannian, Finsler, etc.) (58J60) Optimal transportation (49Q22)
Cites Work
- Unnamed Item
- Unnamed Item
- Metric measure spaces supporting Gagliardo-Nirenberg inequalities: volume non-collapsing and rigidities
- Caffarelli-Kohn-Nirenberg inequality on metric measure spaces with applications
- Sharp geometric and functional inequalities in metric measure spaces with lower Ricci curvature bounds
- The Gagliardo-Nirenberg inequalities and manifolds of non-negative Ricci curvature
- Best constant in Sobolev inequality
- Problèmes isoperimetriques et espaces de Sobolev
- Isoperimetricity for groups and manifolds
- On manifolds with non-negative Ricci curvature and Sobolev inequalities
- Complete manifolds with nonnegative Ricci curvature and almost best Sobolev constant
- The general optimal \(L^{p}\)-Euclidean logarithmic Sobolev inequality by Hamilton--Jacobi equations.
- A mass-transportation approach to sharp Sobolev and Gagliardo-Nirenberg inequalities.
- A Riemannian interpolation inequality à la Borell, Brascamp and Lieb
- Sharp uncertainty principles on Riemannian manifolds: the influence of curvature
- The optimal Euclidean \(L^{p}\)-Sobolev logarithmic inequality.
- Isoperimetric problems for convex bodies and a localization lemma
- Existence and uniqueness of monotone measure-preserving maps
- An Alexandroff-Bakelman-Pucci estimate on Riemannian manifolds
- Rigidity and almost rigidity of Sobolev inequalities on compact spaces with lower Ricci curvature bounds
- Minimising hulls, p-capacity and isoperimetric inequality on complete Riemannian manifolds
- Sharp geometric inequalities for closed hypersurfaces in manifolds with nonnegative Ricci curvature
- The Caffarelli-Kohn-Nirenberg inequalities and manifolds with nonnegative weighted Ricci curvature
- Sharp and rigid isoperimetric inequalities in metric-measure spaces with lower Ricci curvature bounds
- Ricci curvature for metric-measure spaces via optimal transport
- On the geometry of metric measure spaces. I
- The Caffarelli-Kohn-Nirenberg inequality on metric measure spaces
- Sharp isoperimetric and Sobolev inequalities in spaces with nonnegative Ricci curvature
- A note on the critical Laplace equation and Ricci curvature
- On the Best Constant for a Weighted Sobolev-Hardy Inequality
- Riemannian Geometry
- Polar factorization and monotone rearrangement of vector‐valued functions
- Logarithmic Sobolev Inequalities
- Logarithmic Sobolev Inequalities for the Heat-Diffusion Semigroup
- Random walks in a convex body and an improved volume algorithm
- Lectures on Elliptic Partial Differential Equations
- Complete manifolds with non-negative Ricci curvature and the Caffarelli–Kohn–Nirenberg inequalities
- Book Review: Geometry of isotropic convex bodies
- Existence, Uniqueness, and Regularity of Optimal Transport Maps
- Optimal Transport
- Polar factorization of maps on Riemannian manifolds
- Optimal transportation on non-compact manifolds
- Sobolev Inequalities in Manifolds with Nonnegative Curvature
- On the critical \(p\)-Laplace equation
- Stability of Sobolev inequalities on Riemannian manifolds with Ricci curvature lower bounds
- Sharp log-Sobolev inequalities in \(\mathsf{CD}(0, N)\) spaces with applications
This page was built for publication: Sharp Sobolev inequalities on noncompact Riemannian manifolds with \(\mathrm{Ric} \geq 0\) via optimal transport theory