The corona problem with two pieces of data

TL;DR

This paper addresses the corona problem in complex analysis, demonstrating solvability with only two data pieces under certain geometric conditions on the unit ball and pseudoconvex domains.

Contribution

It provides a solution to the corona problem with two pieces of data under specific geometric hypotheses, extending previous results.

Findings

Solved the corona problem with two data pieces under geometric conditions

Extended solvability results to strongly pseudoconvex domains

Identified key geometric hypotheses for solvability

Abstract

We study the corona problem on the unit ball in $\CC^n$, and more generally on strongly pseudoconvex domains in $\CC^n$. When the corona problem has just two pieces of data, and an extra geometric hypothesis is satisfied, then we are able to solve it.