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Eigenvalue estimates for submanifolds of warped product spaces

Published online by Cambridge University Press:  28 June 2013

G. P. BESSA
Affiliation:
Departamento de Matemática, Universidade Federal do Ceará, 60455-760 Fortaleza-CE, Brazil. e-mail: bessa@mat.ufc.br, lucio.mari@libero.it
S. C. GARCÍA–MARTÍNEZ
Affiliation:
Departamento de Matemáticas, Universidad de Murcia, Campus de Espinardo, 30100 Espinardo, Murcia, Spain. e-mail: scarolinagarciam@gmail.com, hectorfabian.ramirez@um.es
L. MARI
Affiliation:
Departamento de Matemática, Universidade Federal do Ceará, 60455-760 Fortaleza-CE, Brazil. e-mail: bessa@mat.ufc.br, lucio.mari@libero.it
H. F. RAMIREZ–OSPINA
Affiliation:
Departamento de Matemáticas, Universidad de Murcia, Campus de Espinardo, 30100 Espinardo, Murcia, Spain. e-mail: scarolinagarciam@gmail.com, hectorfabian.ramirez@um.es

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 fC(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.

Type
Research Article
Copyright
Copyright © Cambridge Philosophical Society 2013 

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