# Eigenvaluues monotonicity of Witten-Laplacian along the mean curvature flow

## TL;DR

This paper investigates how the first eigenvalue of the Witten-Laplace operator evolves along the mean curvature flow, revealing monotonic properties that could inform geometric analysis.

## Contribution

It derives the evolution equation for the eigenvalue and identifies monotonic quantities during the mean curvature flow.

## Key findings

- Derived the evolution equation for the first eigenvalue.
- Identified monotonic quantities under the flow.
- Provided insights into spectral properties during geometric evolution.

## Abstract

In this paper, we derive the evolution equation for the first eigenvalue of the Witten-Laplace operator acting on the space of functions along the mean curvature flow on a closed oriented manifold. We show some interesting monotonic quantities under the mean curvature flow.