The Euclidean elliptic complex

Nicholas Hanges, Howard Jacobowitz

Research output: Contribution to journalArticlepeer-review

3 Scopus citations


Let Ω ⊂ ℂm × ℝn be an open subset with smooth boundary. The de Rham complex of ℝn and the Dolbeaut complex of ℂm induce a natural elliptic complex on Ω D : Λp(Ω) → Λp+1(Ω), p = 0, . . . , m + n. D induces a natural involutive (formally integrable) structure, Db, on the boundary of Ω. Let Σ ⊂ ∂Ω be the set of points where Db is not elliptic. We assume that the Levi form is positive definite at each point of Σ. Away from Σ we make no assumption. Under these conditions we show that the cohomology for D vanishes in dimension p ≥ 1.

Original languageEnglish (US)
Pages (from-to)753-770
Number of pages18
JournalIndiana University Mathematics Journal
Issue number3
StatePublished - 1997

All Science Journal Classification (ASJC) codes

  • General Mathematics


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