JournalsjemsVol. 24, No. 10pp. 3557–3595

A cone restriction estimate using polynomial partitioning

  • Yumeng Ou

    University of Pennsylvania, Philadelphia, USA
  • Hong Wang

    UCLA, Los Angeles, USA
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Abstract

We obtain an improved Fourier restriction estimate for a truncated cone using the method of polynomial partitioning in dimension n3n\geq 3, which in particular solves the cone restriction conjecture for n=5n=5, and recovers the sharp range for 3n43\leq n\leq 4. The main ingredient of the proof is a kk-broad estimate for the cone extension operator, which is a weak version of the kk-linear cone restriction conjecture for 2kn2\leq k\leq n.

Cite this article

Yumeng Ou, Hong Wang, A cone restriction estimate using polynomial partitioning. J. Eur. Math. Soc. 24 (2022), no. 10, pp. 3557–3595

DOI 10.4171/JEMS/1168