# Magnetic fields and boundary conditions in spectral and asymptotic analysis

## TL;DR

This paper explores the spectral properties of magnetic Laplacians, focusing on eigenvalue asymptotics in cornered domains and threshold analysis of fibered operators, connecting these through model problems in unbounded domains.

## Contribution

It provides new insights into the eigenvalue asymptotics and threshold behavior of magnetic Laplacians in complex geometries and fibered structures.

## Key findings

- Asymptotic formulas for low-lying eigenvalues in cornered domains
- Analysis of spectral thresholds in fibered magnetic operators
- Connections between unbounded domain models and spectral properties

## Abstract

This memoir is devoted to a part of the results from the author about two topics: in the first part, the asymptotics of the low-lying eigenvalues of Schr\"odinger operators in domains that may have corners, and in the second part, the analysis of the thresholds of a class of fibered operators. The main common object is the magnetic Laplacian, and the two parts are connected through the study of model problems in unbounded domains.