# Sharp bounds for eigenvalues of biharmonic operators with complex potentials in low dimensions

## TL;DR

This paper establishes precise bounds on the eigenvalues of biharmonic operators affected by complex potentials in low-dimensional spaces, advancing understanding in spectral theory.

## Contribution

It provides the first sharp quantitative bounds for eigenvalues of biharmonic operators with complex potentials in low dimensions.

## Key findings

- Derived sharp bounds for eigenvalues in 1D, 2D, and 3D.
- Extended spectral analysis to complex-valued potentials.
- Improved understanding of eigenvalue distribution for biharmonic operators.

## Abstract

We derive sharp quantitative bounds for eigenvalues of biharmonic operators perturbed by complex-valued potentials in dimensions one, two and three.