Regular multi-types and the Bloom conjecture

Xiaojun Huang, Wanke Yin

Research output: Contribution to journalArticlepeer-review

4 Scopus citations


We prove that the commutator type, the regular contact type and the Levi form type of order s=(n−2) are the same for a smooth pseudoconvex real hypersurface in Cn with n≥3. In particular, this provides, in the case of complex dimension three, a complete solution of a long standing conjecture of Bloom formulated in his famous and important 1981 paper [12]. When n≥4, our theorem provides the first result along the lines of the Bloom conjecture in any dimensions in a case where the pseudoconvexity assumption of the hypersurface starts to be crucial.

Original languageEnglish (US)
Pages (from-to)69-98
Number of pages30
JournalJournal des Mathematiques Pures et Appliquees
StatePublished - Feb 2021

All Science Journal Classification (ASJC) codes

  • General Mathematics
  • Applied Mathematics


  • Bloom conjecture
  • CR singular submanifolds
  • Finite type conditions for pseudoconvex smooth real hypersurfaces
  • Hopf lemma
  • Nagano theory
  • Normalization of CR vector fields


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