Ana Vargas

Title: Some results on restriction of the Fourier transform to surfaces with negative curvature

Abstract: We consider the problem of restriction of the Fourier transform to surfaces in $\mathbb R^3$ with nonvanishing gaussian curvature. The methods developed since the nineties (bilinear, multilinear or polynomial partitioning), seem to find geometrical obstacles when applied to surfaces of negative curvature. Only in the particular case of the saddle the results known are similar to the theorems for surfaces of positive curvature. In joint work with Detlef Müller and Stefan Buschenhenke, we have initiated the study of perturbations of the saddle with those techniques, obtaining some results in the case of 1-variable perturbations.

Slides