On the Initial Value Problem for Causal Variational Principles

TL;DR

This paper formulates and analyzes the initial value problem for causal variational principles on compact metric spaces, establishing existence and uniqueness of solutions with illustrative examples.

Contribution

It introduces a framework for the initial value problem in causal variational principles and proves key existence and uniqueness results.

Findings

Existence of solutions is established.

Uniqueness of solutions is proven.

Simple examples illustrate the theoretical results.

Abstract

We formulate the initial value problem for causal variational principles in the continuous setting on a compact metric space. The existence and uniqueness of solutions is analyzed. The results are illustrated by simple examples.