On Fourier restriction for finite-type perturbations of the hyperboloid
Abstract
In this note, we continue our research on Fourier restriction for hyperbolic surfaces, by studying local perturbations of the hyperbolic paraboloid z=xy, which are of the form z=xy+h(y), where h(y) is a smooth function of finite type. Our results build on previous joint work in which we have studied the case h(y)=y3/3 by means of the bilinear method. As it turns out, the understanding of that special case becomes also crucial for the treatment of arbitrary finite type perturbation terms h(y).
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