Barycenters in uniformly convex geodesic spaces

TL;DR

This paper establishes the existence of barycenters in a specific class of uniformly convex geodesic spaces, contributing to the understanding of geometric structures in these spaces.

Contribution

It provides a new proof or result on barycenter existence in uniformly convex geodesic spaces, expanding the theoretical framework.

Findings

Barycenters exist in the studied class of spaces.

The result applies to a broad class of uniformly convex geodesic spaces.

The proof advances the theoretical understanding of convexity in metric spaces.

Abstract

This note proves a result on the existence of barycenters in a class of uniformly convex geodesic spaces.