Eigenvalue bounds for the Steklov problem on differential forms in warped product manifolds

Key Points

• The research reveals that warped product manifolds can significantly influence eigenvalue bounds for differential forms, enhancing our understanding of spectral geometry.
• The study provides Escobar type lower bounds for warped product manifolds with non-negative Ricci curvature, while also detailing certain sharp bounds for specific geometric configurations.
• Comparisons reveal distinct differences when analyzing the eigenvalue bounds of differential forms versus those of functions, spotlighting the role of topology in spectral characteristics.
• Using various techniques, the research uncovers pertinent eigenvalue relationships and geometric constraints, which can inform future studies in spectral theory and manifold geometry.