# Zhong-Yang type eigenvalue estimate with integral curvature condition

## TL;DR

This paper establishes a precise lower bound for the first eigenvalue of the Laplacian on closed Riemannian manifolds using integral Ricci curvature conditions, extending classical estimates.

## Contribution

It introduces a sharp Zhong-Yang type eigenvalue estimate under integral Ricci curvature bounds, broadening the scope of eigenvalue estimates in Riemannian geometry.

## Key findings

- Proves a sharp lower bound for the first eigenvalue
- Extends classical estimates to integral curvature conditions
- Provides new tools for geometric analysis

## Abstract

We prove a sharp Zhong-Yang type eigenvalue lower bound for closed Riemannian manifolds with control on integral Ricci curvature.