Eigenvalue estimates for submanifolds of warped product spaces

TL;DR

This paper establishes lower bounds for the fundamental tone and analyzes the essential spectrum of minimal submanifolds immersed in warped product spaces, advancing spectral geometry understanding.

Contribution

It provides new eigenvalue estimates and spectral analysis results specifically for minimal submanifolds in warped product ambient spaces.

Findings

Lower bounds for the fundamental tone of open sets in minimal submanifolds.

Analysis of the essential spectrum of these minimal submanifolds.

Spectral geometric properties of minimal submanifolds in warped products.

Abstract

We give lower bounds for the fundamental tone of open sets in minimal submanifolds immersed into warped product spaces of type $N^n \times_f Q^q$, where $f \in C^\infty(N)$. We also study the essential spectrum of these minimal submanifolds.