We give a new proof of the almost sharp Moser–Trudinger inequality on smooth compact Riemannian manifolds based on the sharp Moser inequality on Euclidean spaces and generalize it to Riemannian manifolds with continuous metrics and to higher order Sobolev spaces on manifolds with boundary under several boundary conditions. These generalizations can be applied to fourth order Q curvature equations in dimension 4.
- Almost sharp Moser–Trudinger inequality
- Concentration compactness principle
- Defect measure
- Paneitz operator
- Q curvature equations
ASJC Scopus subject areas
- Geometry and Topology