On the topology of surfaces with the generalised simple lift property

TL;DR

This paper investigates the geometric properties of surfaces possessing the generalized simple lift property, extending prior research and motivated by minimal lamination limits of minimal disks.

Contribution

It generalizes previous results on surface topology with the simple lift property, broadening understanding of minimal lamination limits.

Findings

Surfaces with the generalized simple lift property are characterized.

Connections between minimal laminations and surface topology are established.

New classifications of surfaces based on lift properties are proposed.

Abstract

In this paper, we study the geometry of surfaces with the generalised simple lift property. This work generalises previous results by Bernstein and Tinaglia, and it is motivated by the fact that leaves of a minimal lamination obtained as a limit of a sequence of properly embedded minimal disks satisfy the generalised simple lift property.