Title: Strichartz Inequalities on Compact Manifolds
Abstract: Strichartz inequalities on Rn follow from a simple dispersion estimate and interpolation, and are optimal. The story changes dramatically on compact domains, where such an estimate can never hold. However, it is a great triumph of Bourgain that intermediate estimates hold at all on the Torus, and the ideas behind his proofs have been a driving force behind much of modern Harmonic Analysis. In this talk we will discuss the case of an arbitrary compact manifold without boundary and develop lossy-Strichartz estimates that somehow end up being sharp on certain manifolds (like the sphere!). This talk is a sequel to a prior talk I gave but won't require any knowledge of the other. Strichartz inequalities on Rn follow from a simple dispersion estimate and interpolation, and are optimal. The story changes dramatically on compact domains, where such an estimate can never hold. However, it is a great triumph of Bourgain that intermediate estimates hold at all on the Torus, and the ideas behind his proofs have been a driving force behind much of modern Harmonic Analysis. In this talk we will discuss the case of an arbitrary compact manifold without boundary and develop lossy-Strichartz estimates that somehow end up being sharp on certain manifolds (like the sphere!). This talk is a sequel to a prior talk I gave but won't require any knowledge of the other.
