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Global restriction estimates for elliptic hyperboloids

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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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  1. Department of Mathematics, University of British Columbia, 1984 Mathematics Road, Vancouver, BC, V6T 1Z2, Canada

    Benjamin Baker Bruce

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  1. Benjamin Baker Bruce
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Correspondence to Benjamin Baker Bruce.

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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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