Some recent progress on sharp Fourier restriction theory
arXiv:1701.06895
Abstract
The purpose of this note is to discuss several results that have been obtained in the last decade in the context of sharp adjoint Fourier restriction/Strichartz inequalities. Rather than aiming at full generality, we focus on several concrete examples of underlying manifolds with large groups of symmetries, which sometimes allows for simple geometric proofs. We mention several open problems along the way, and include an appendix on integration on manifolds using delta calculus.
22 pages, 5 figures, survey paper
References in corpus (10)
- Maximizers for the Strichartz Inequalities for the Wave Equation
- Nonexistence of extremals for the adjoint restriction inequality on the hyperboloid
- On extremizing sequences for the adjoint restriction inequality on the cone
- A sharp trilinear inequality related to Fourier restriction on the circle
- A sharp bilinear estimate for the Klein-Gordon equation in arbitrary space-time dimensions
- Analyticity of extremisers to the Airy Strichartz inequality
- On sharp bilinear Strichartz estimates of Ozawa-Tsutsumi type
- Optimal constants and extremisers for some smoothing estimates
- Nonexistence of extremizers for certain convex curves
- Linear profile decompositions for a family of fourth order Schrödinger equations