Work

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

Year: 2025

Type: article

Abstract: We consider the Steklov problem on differential $$p\text {-}$$ p - forms defined by Karpukhin and present geometric eigenvalue bounds in the setting of warped product manifolds in various scenarios. In particular, we obtain Escobar type lower bounds for warped product manifolds with non-negative Ricci curvature and strictly convex boundary, and certain sharp bounds for hypersurfaces of revolution, among others. We compare and contrast the behaviour with known results in the case of functions (i.e., $$0\text {-}$$ 0 - forms), highlighting the influence of the underlying topology on the spectrum for $$p\text {-}$$ p - forms in general.

Source: Annales mathématiques du Québec

DOI: 10.1007/s40316-025-00255-w

Author: Tirumala Chakradhar

Institution: University of Bristol

Language: English

Topic: Spectral Theory in Mathematical Physics

Subfield: Mathematical Physics

Field: Mathematics

Domain: Physical Sciences

Open Access status: hybrid

Estimated APC paid: $3,190

Funders: University of Bristol, Engineering and Physical Sciences Research Council