Eigenvalue estimate for the basic Laplacian on manifolds with foliated boundary View Full Text


Ontology type: schema:ScholarlyArticle      Open Access: True


Article Info

DATE

2018-11

AUTHORS

Fida El Chami, Georges Habib, Ola Makhoul, Roger Nakad

ABSTRACT

On a compact Riemannian manifold whose boundary is endowed with a Riemannian flow, we give a sharp lower bound for the first eigenvalue of the basic Laplacian acting on basic 1-forms. The equality case gives rise to a particular geometry of the flow and of the boundary. Namely, we prove that the flow is a local product and the boundary is η-umbilical. This allows to characterize the quotient of R×B′ by some group Γ as the limiting manifold. Here B′ denotes the unit closed ball. Finally, we deduce several rigidity results describing the product S1×Sn as the boundary of a manifold. More... »

PAGES

765-784

References to SciGraph publications

Identifiers

URI

http://scigraph.springernature.com/pub.10.1007/s11587-017-0339-7

DOI

http://dx.doi.org/10.1007/s11587-017-0339-7

DIMENSIONS

https://app.dimensions.ai/details/publication/pub.1092065695


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