The sharp Sobolev inequality on metric measure spaces with lower Ricci curvature bounds. (English) Zbl 1333.53050
The author shows that the sharp Sobolev inequality holds for certain metric measure spaces in the form known for some Riemannian manifolds. The proof follows the pattern of the known result.
Reviewer: Dumitru Motreanu (Perpignan)
MSC:
| 53C23 | Global geometric and topological methods (à la Gromov); differential geometric analysis on metric spaces |
| 53C21 | Methods of global Riemannian geometry, including PDE methods; curvature restrictions |
| 26D10 | Inequalities involving derivatives and differential and integral operators |
| 49J52 | Nonsmooth analysis |
| 46E35 | Sobolev spaces and other spaces of “smooth” functions, embedding theorems, trace theorems |
Keywords:
sharp Sobolev inequality; Nash inequality; metric measure spaces; curvature-dimension conditionReferences:
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