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 â̂̂ 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.
Eigenvalue estimates for submanifolds of warped product spaces / P. Bessa Gregório, C. García–Martínez Sandra, L. Mari, F. Ramirez–Ospina Hector. - In: MATHEMATICAL PROCEEDINGS OF THE CAMBRIDGE PHILOSOPHICAL SOCIETY. - ISSN 0305-0041. - 156:01(2014 Jan), pp. 25-42. [10.1017/S0305004113000443]
Eigenvalue estimates for submanifolds of warped product spaces
L. MariPenultimo
;
2014
Abstract
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 â̂̂ 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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