58 research outputs found
On extremizing sequences for the adjoint restriction inequality on the cone
It is known that extremizers for the to adjoint Fourier
restriction inequality on the cone in exist. Here we show that
nonnegative extremizing sequences are precompact, after the application of
symmetries of the cone. If we use the knowledge of the exact form of the
extremizers, as found by Carneiro, then we can show that nonnegative
extremizing sequences converge, after the application of symmetries.Comment: 27 pages. Includes referee comment
Nonexistence of extremals for the adjoint restriction inequality on the hyperboloid
We study the problem of existence of extremizers for the to
adjoint Fourier restriction inequalities on the hyperboloid in dimensions 3 and
4, in which cases is an even integer. We will use the method developed by
Foschi to show that extremizers do not exist.Comment: 32 pages. Correction for Theorem 1.2 and Proposition 7.5 and addition
of Remark 1.
- …