# Mean Value Theorems for Riemannian Manifolds via the Obstacle Problem

## TL;DR

This paper develops the obstacle problem theory on Riemannian manifolds and uses it to prove a broad mean value theorem that applies widely without weights.

## Contribution

It introduces a new approach to the obstacle problem on Riemannian manifolds and establishes a general mean value theorem without weights.

## Key findings

- Mean value theorem valid for many Riemannian manifolds
- No weights needed in the integral for the theorem
- Broad applicability of the developed theory

## Abstract

We develop some of the basic theory for the obstacle problem on Riemannian Manifolds, and we use it to establish a mean value theorem. Our mean value theorem works for a very wide class of Riemannian manifolds and has no weights at all within the integral.