A cone restriction estimate using polynomial partitioning

Yumeng Ou, Hong Wang

Research output: Contribution to journalArticlepeer-review


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

Original languageEnglish (US)
Pages (from-to)3557-3595
Number of pages39
JournalJournal of the European Mathematical Society
Issue number10
StatePublished - 2022


  • polynomial method
  • Restriction estimate

ASJC Scopus subject areas

  • General Mathematics
  • Applied Mathematics


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