A Rigidity Condition for Holomorphic Generator in Strongly Convex Domains

TL;DR

This paper establishes a boundary behavior condition that ensures the infinitesimal generator of a holomorphic semigroup in strongly convex domains is zero, contributing to the understanding of complex dynamics in such domains.

Contribution

It introduces a new boundary condition criterion that guarantees the vanishing of the holomorphic generator in strongly convex domains.

Findings

Boundary condition ensures generator vanishes

Provides a criterion for generator behavior

Advances understanding of holomorphic semigroup dynamics

Abstract

In this paper I give a condition, in terms of boundary behaviour, that forces the infinitesimal generator of a one-parameter semigroup of holomorphic maps to vanish.