Wolff-Denjoy theorems in non-smooth convex domains

TL;DR

This paper extends the Wolff-Denjoy theorem to non-smooth strictly convex and weakly convex domains using a novel proof technique, broadening its applicability in complex analysis.

Contribution

Provides a new, concise proof of Wolff-Denjoy theorem applicable to non-smooth convex domains, including weakly convex cases, without boundary smoothness assumptions.

Findings

Wolff-Denjoy theorem holds in non-smooth strictly convex domains.

The theorem is also valid for weakly convex domains.

Proof techniques do not require boundary smoothness.

Abstract

We give a short proof of Wolff-Denjoy theorem for (not necessarily smooth) strictly convex domains. With similar techniques we are also able to prove a Wolff-Denjoy theorem for weakly convex domains, again without any smoothness assumption on the boundary.