Pure and Applied Mathematics Quarterly

Volume 18 (2022)

Number 2

Special issue in honor of Joseph J. Kohn on the occasion of his 90th birthday

Guest Editors: J.E. Fornaess, Stanislaw Janeczko, Duong H. Phong, and Stephen S.T. Yau

Sums of CR and projective dual CR functions

Pages: 371 – 394

DOI: https://dx.doi.org/10.4310/PAMQ.2022.v18.n2.a1

Authors

David E. Barrett (Department of Mathematics, University of Michigan, Ann Arbor, Mich., U.S.A.)

Dusty E. Grundmeier (Department of Mathematics, Harvard University, Cambridge, Massachusetts, U.S.A.)

Abstract

A smooth, strongly $\mathbb{C}$-convex, real hypersurface $S$ in $\mathbb{CP}^n$ admits a projective dual CR structure in addition to the standard CR structure. Given a smooth function $u$ on $S$, we provide characterizations for when u can be decomposed as a sum of a CR function and a dual CR function. Following work of Lee on pluriharmonic boundary values, we provide a characterization using differential forms. We further provide a characterization using tangential vector fields in the style of Audibert and Bedford.

2010 Mathematics Subject Classification

32V10

Received 15 March 2021

Received revised 5 August 2021

Accepted 13 August 2021

Published 13 May 2022