Abstract
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 language | English (US) |
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Article number | 18 |
Journal | Complex Analysis and its Synergies |
Volume | 8 |
Issue number | 4 |
DOIs | |
State | Published - Dec 2022 |
Keywords
- Complex Green operator
- High codimension
- Quadric submanifolds
- Tangential Cauchy–Riemann operator
ASJC Scopus subject areas
- Analysis
- Mathematics (miscellaneous)
- Numerical Analysis