Estimates for the first eigenvalue of the drifting Laplacian on embedded hypersurfaces

Abstract

Abstract. For an (n − 1)-dimensional compact orientable smooth metric measure space ` M, g, e−f dvg ́ embedded in an n-dimensional compact orientable Riemannian manifold N , we successfully give a lower bound for the first nonzero eigenvalue of the drifting Laplacian on M , provided the Ricci curvature of N is bounded from below by a positive constant and the weighted function f on M satisfies two constraints.