Twistor theory and the harmonic hull

TL;DR

This paper employs twistor theory to characterize the harmonic hull of open subsets in real space, identifying it as the domain where harmonic functions can be analytically continued in complex space.

Contribution

It introduces a novel application of twistor theory to determine the harmonic hull as the domain of analytic continuation for harmonic functions.

Findings

Harmonic hull is identified via twistor theory.

Harmonic functions extend analytically within the harmonic hull.

The method applies to connected open subsets in R^{2m} for m ≥ 2.

Abstract

We use twistor theory to identify the harmonic hull of an arbitrary connected open subset U of R^{2m} for m at least 2. It is the natural domain of analytic continuation in C^{2m} for harmonic functions on U.