Work

Topology and bottom spectrum of transversally negatively curved foliations

Year: 2025

Type: article

Abstract: We show that for any Riemannian foliation with a simply connected and negatively curved leaf space the normal exponential map of a leaf is a diffeomorphism. As an application, if the leaves are furthermore minimal submanifolds, we give a sharp estimate for the bottom of the spectrum of such a Riemannian manifold. Our proof of the spectral estimate also yields an estimate for the bottom of the spectrum of the horizontal Laplacian.

Source: Annals of Global Analysis and Geometry

DOI: 10.1007/s10455-025-10020-5

Author: Fabrice Baudoin

Institution: Aarhus University

Language: English

Topic: Geometric Analysis and Curvature Flows

Subfield: Applied Mathematics

Field: Mathematics

Domain: Physical Sciences

Open Access status: hybrid

Estimated APC paid: $3,190

Funders: Aarhus Universitet, Villum Fonden