Analysis on quadrics

Albert Boggess, Andrew Raich

Research output: Contribution to journalArticlepeer-review


This paper surveys recent progress on the analysis of the □ b operator on quadric submanifolds of Cn× Cm. We focus our discussion on the (relative) fundamental solution to □ b on quadric submanifolds of arbitrary codimension. We summarize known results regarding □ b-invariance of mappings, necessary and sufficient conditions for solvability and hypoellipticity for □ b, and we describe the Lp regularity of the complex Green operator on quadrics with nonvanishing Levi form. We discuss the ramifications of these results for many examples of quadrics of codimension 1 and 2.

Original languageEnglish (US)
Article number18
JournalComplex Analysis and its Synergies
Issue number4
StatePublished - Dec 2022


  • Complex Green operator
  • High codimension
  • Quadric submanifolds
  • Tangential Cauchy–Riemann operator

ASJC Scopus subject areas

  • Analysis
  • Mathematics (miscellaneous)
  • Numerical Analysis


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