An open problem in complex analytic geometry arising in harmonic analysis

TL;DR

This paper discusses an open problem in complex analytic geometry related to harmonic analysis, focusing on Fourier integral operators and PDE regularity, presenting partial results and a conjecture on affine fibrations.

Contribution

It introduces a new open problem in complex analysis linked to harmonic analysis and PDEs, with initial results and a conjecture on affine fibrations.

Findings

Presented a self-contained discussion of the open problem.

Provided partial results towards solving the problem.

Formulated a conjecture on the structure of affine fibrations.

Abstract

In this paper, an open problem in the multidimensional complex analysis is pesented that arises in the investigation of the regularity properties of Fourier integral operators and in the regularity theory for hyperbolic partial differential equations. The problem is discussed in a self-contained elementary way and some results towards its resolution are presented. A conjecture concerning the structure of appearing affine fibrations is formulated.