Convexity properties of coverings of 1-convex surfaces

TL;DR

This paper investigates the convexity properties of coverings of 1-convex surfaces, demonstrating that some universal coverings lack the discrete disk property, which challenges previous assumptions about their convexity behavior.

Contribution

It establishes the existence of a 1-convex surface with a universal covering that does not satisfy the discrete disk property, revealing new insights into convexity properties.

Findings

Existence of a 1-convex surface with a universal covering lacking the discrete disk property

Challenges previous beliefs about convexity of coverings of 1-convex surfaces

Provides a counterexample in the study of convexity properties

Abstract

We prove that there exists a 1-convex surface whose universal covering does not satisfy the discrete disk property.