# An Estimate of the First Eigenvalue of a Schr\"odinger Operator on Closed Surfaces

## TL;DR

This paper provides an estimate for the first eigenvalue of a Schrödinger operator, specifically the Jacobi operator, on closed surfaces, extending previous work by Schoen and Yau.

## Contribution

It introduces a new eigenvalue estimate for the Jacobi operator on minimal surfaces in flat 3-space, building on Schoen-Yau's foundational work.

## Key findings

- Derived a new lower bound for the first eigenvalue
- Extended eigenvalue estimates to minimal surfaces in flat 3-space
- Built upon Schoen-Yau's theoretical framework

## Abstract

Based on the work of Schoen-Yau, we derive an estimate of the first eigenvalue of a Schr\"odinger Operator (the Jaocbi operator of minimal surfaces in flat 3-spaces) on surfaces.