The Greene-Krantz Conjecture in Dimension Two

TL;DR

This paper proves the Greene-Krantz conjecture for convex domains in two complex dimensions, utilizing subelliptic estimates for the ar problem, thus advancing understanding in several complex variables.

Contribution

It provides the first proof of the Greene-Krantz conjecture in ^2 for convex domains, employing novel techniques based on subelliptic estimates.

Findings

Proof of the Greene-Krantz conjecture in ^2 for convex domains

Introduction of subelliptic estimate methods to the conjecture

Enhanced understanding of boundary regularity in complex analysis

Abstract

We give a proof of the Greene-Krantz conjecture on convex domains in $\CC^2$. Curiously, the proof technique depends on subelliptic estimates for the $\bar{\partial}$ problem.