Abstract
We prove global Fourier restriction estimates for elliptic, or two-sheeted, hyperboloids of arbitrary dimension \(d \ge 2\), extending recent joint work with D. Oliveira e Silva and B. Stovall. Our results are unconditional in the (adjoint) bilinear range, \(q > \frac{2(d+3)}{d+1}\), and extend conditionally upon further progress toward the local restriction conjecture for elliptic surfaces.
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Acknowledgements
The author thanks his advisor Betsy Stovall for suggesting this project and acknowledges support from NSF grant DMS-1653264.
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Bruce, B.B. Global restriction estimates for elliptic hyperboloids. Math. Z. 301, 2111–2128 (2022). https://doi.org/10.1007/s00209-022-02988-8
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DOI: https://doi.org/10.1007/s00209-022-02988-8