# Monotone Relations in Hadamard Spaces

## TL;DR

This paper introduces the concept of $\

## Contribution

It defines the $\

## Key findings

- Characterizes flat Hadamard spaces via the $\
- paper_type":"theoretical"}}}# Answer {
- contribution

## Abstract

In this paper, the notion of $\mathcal{W}$-property for subsets of $X\times X^{\lozenge}$ is introduced and investigated, where $X$ is an Hadamard space and $X^{\lozenge}$ is its linear dual space. It is shown that an Hadamard space $X$ is flat if and only if $X\times X^{\lozenge}$ has $\mathcal{W}$-property. Moreover, the notion of monotone relation from an Hadamard space to its linear dual space is introduced. Finally, a characterization result for monotone relations with $\mathcal{W}$-property (and hence in flat Hadamard spaces) is proved.