Propagation at the vertex of a sector

TL;DR

This paper investigates the conditions under which holomorphic functions can be extended across boundary points of infinite type with cusped sectors, focusing on the sector property at the vertex.

Contribution

It introduces a sector property framework for analyzing holomorphic extension at cusped, infinite-type boundary points, advancing understanding of boundary regularity.

Findings

Holomorphic extension is characterized by the sector property at cusped boundary points.

The sector property provides necessary and sufficient conditions for extension.

Analysis of infinite type points with cusped sectors enhances boundary regularity theory.

Abstract

We discuss holomorphic extension across a boundary point in terms of sector property. The point is of infinite type and the sector is accordingly "cusped" at the vertex.