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arXiv · 2109.01199

Sums of CR and projective dual CR functions

David E. Barrett·Dusty E. Grundmeier
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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.

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David E. Barrett, Dusty E. Grundmeier. 2021-09-02. Sums of CR and projective dual CR functions. https://arxiv.org/abs/2109.01199

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