Monotonicity of Subelliptic Estimates on Rigid Pseudoconvex Domains

TL;DR

This paper proves that subelliptic estimates on rigid pseudoconvex domains increase monotonically and shows that for finite type rigid monomial domains, the sharp estimate is the reciprocal of the type.

Contribution

It establishes the monotonicity property of subelliptic estimates and relates the sharp estimate to the D'Angelo type for rigid monomial domains.

Findings

Monotonicity of subelliptic estimates on rigid pseudoconvex domains.

Sharp subelliptic estimate equals the reciprocal of the D'Angelo type for finite type domains.

Application to rigid monomial domains of finite type.

Abstract

This paper presents monotonicity of subelliptic estimates on rigid pseudoconvex domains. As an application of monotonicity, we will show that if a rigid monomial domain is of finite type in the D'Angelo's sense, then the sharp subelliptic estimate of this domain equals the reciprocal of the type.