Eigenvalue estimates for submanifolds of warped product spaces

Eigenvalue estimates for submanifolds of warped product spaces

In this paper, we give lower bounds for the fundamental tone of open sets in minimal submanifolds immersed into warped product spaces of type Nn ×f Qq, where f ∈ C∞(N). This setting allows us to deal, among other things, with minimal submanifolds bounded by cylinders, cones, spheres and pseudo-hyper...

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Veröffentlicht in:Mathematical proceedings of the Cambridge Philosophical Society 2014-01, Vol.156 (1), p.25-42
Hauptverfasser: BESSA, G. P., GARCÍA–MARTÍNEZ, S. C., MARI, L., RAMIREZ–OSPINA, H. F.
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Boundaries
Eigenvalues
Geometry
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container_title Mathematical proceedings of the Cambridge Philosophical Society
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GARCÍA–MARTÍNEZ, S. C.
MARI, L.
RAMIREZ–OSPINA, H. F.
description In this paper, we give lower bounds for the fundamental tone of open sets in minimal submanifolds immersed into warped product spaces of type Nn ×f Qq, where f ∈ C∞(N). This setting allows us to deal, among other things, with minimal submanifolds bounded by cylinders, cones, spheres and pseudo-hyperbolic spaces where most of these examples are not covered in the literature. Applications also include the study of the essential spectrum of hyperbolic graphs over compact regions of the boundary at infinity.
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source Cambridge University Press Journals Complete
subjects Boundaries
Eigenvalues
Geometry
title Eigenvalue estimates for submanifolds of warped product spaces
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