On $\mathsf{CD}$ spaces with nonnegative curvature outside a compact set

TL;DR

This paper extends the understanding of non-branching CD spaces with nonnegative curvature outside a compact set by establishing a ball covering property and bounding the number of ends, contributing to geometric analysis.

Contribution

It adapts Liu's work to prove a ball covering property and derives bounds on the number of ends for non-branching CD spaces with nonnegative curvature outside a compact set.

Findings

Established a ball covering property for the spaces.

Obtained uniform bounds on the number of ends.

Extended geometric analysis techniques to these spaces.

Abstract

In this paper we adapt work of Z.-D. Liu to prove a ball covering property for non-branching $\mathsf{CD}$ spaces with nonnegative curvature outside a compact set. As a consequence we obtain uniform bounds on the number of ends of such spaces.