Rudin's Theorem and Projective Hulls

TL;DR

This paper explores a generalization of Rudin's theorem on analytic functions, extending it from the unit disk to the punctured disk using the concept of projective hulls in complex projective space.

Contribution

It introduces a conjecture extending Rudin's theorem to punctured disks and proves a special case utilizing projective hulls, linking complex analysis and algebraic geometry.

Findings

Proposes a conjecture generalizing Rudin's theorem.

Proves a special case using projective hulls.

Connects complex analysis with algebraic geometry concepts.

Abstract

Walter Rudin, in 1966, characterized analytic functions in the unit disk in terms of the maximum principle relative to the boundary. We conjecture a generalization of this result when the disk is replaced by the punctured disk, and we prove a special case of this conjecture, making use of the notion of projective hull in P^n introduced by R. Harvey and B. Lawson.