Bilinear restriction estimates for surfaces of codimension bigger than one

TL;DR

This paper establishes sharp bilinear restriction estimates for higher codimension surfaces in ^n, extending the understanding of restriction phenomena beyond hypersurfaces like spheres and paraboloids.

Contribution

It provides the first sharp bilinear restriction estimates for general higher codimension surfaces, and derives linear estimates in special cases.

Findings

Sharp bilinear restriction estimates for higher codimension surfaces

Application of bilinear results to obtain linear estimates in specific cases

Extension of restriction theory beyond hypersurfaces

Abstract

In connection with the restriction problem in $\mathbb R^n$ for hypersurfaces including the sphere and paraboloid, the bilinear (adjoint) restriction estimates have been extensively studied. However, not much is known about such estimates for surfaces with codimension (and dimension) larger than one. In this paper we show sharp bilinear $L^2 \times L^2 \to L^q$ restriction estimates for general surfaces of higher codimension. In some special cases, we can apply these results to obtain the corresponding linear estimates.