Pinching of the first eigenvalue for second order operators on hypersurfaces of the Euclidean space

Abstract

We prove stability results associated with upper bounds for the first eigenvalue of certain second order differential operators of divergence-type on hypersurfaces of the Euclidean space. We deduce some applications to $r$-stability as well as to almost-Einstein hypersurfaces.

18 pages. Discussions are welcome

References in corpus (1)

• Quantitative oscillation estimates for almost-umbilical closed hypersurfaces in Euclidean space

Cited by in corpus (2)

• Absence of bubbling phenomena for non convex anisotropic nearly umbilical and quasi Einstein hypersurfaces
• Stability from rigidity via umbilicity