Necessary geometric and analytic conditions for general estimates in the $\dib$-Neumann problem

TL;DR

This paper investigates the geometric and analytic conditions necessary for general estimates in the $ar{ ext{d}}$-Neumann problem, linking boundary contact order and Levi form bounds.

Contribution

It establishes that certain estimates imply specific geometric and analytic boundary conditions, advancing understanding of the $ar{ ext{d}}$-Neumann problem.

Findings

Estimate implies upper bound on contact order of complex curves with boundary.

Estimate implies lower bound on Levi form rate for weights.

Connects geometric boundary properties with analytic estimates.

Abstract

We show that a general estimate in the $\dib$-Neumann problem implies a upper bound on the order of contact of a complex curve with the boundary and a lower bound on the rate of the Levi form of a bounded family of weights.