Nowhere differentiable functions of analytic type on products of finitely connected planar domains

TL;DR

This paper proves that generically, functions of analytic type on products of finitely connected planar domains are nowhere differentiable on their boundary, using advanced complex analysis tools.

Contribution

It introduces a novel combination of Laurent decomposition, Mergelyan's theorem, and Baire's category theorem to establish generic boundary nowhere differentiability.

Findings

Functions are generically nowhere differentiable on the boundary

Uses advanced complex analysis techniques for proof

Applicable to products of finitely connected planar domains

Abstract

Using Laurent decomposition and Mergelyan's theorem combined with Baire's category theorem, we prove generic nowhere differentiability on the distinguished boundary of functions of analytic type on products of planar domains bounded by finitely many disjoint Jordan curves. The parametrization of the boundaries are those induced by the natural Riemann maps.