Abstract
We find out upper bounds for the first eigenvalue of the stability operator for compact constant mean curvature surfaces immersed into certain 3-dimensional Riemannian spaces, in particular into homogeneous 3-manifolds. As an application we derive some consequences for strongly stable surfaces in such ambient spaces. Moreover, we also get a characterization of Hopf tori in certain Berger spheres.
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This work was partially supported by MINECO (Ministerio de Economía y Competitividad) and FEDER (Fondo Europeo de Desarrollo Regional) project MTM2012-34037 and Fundación Séneca project 04540/GERM/06, Spain. This research is a result of the activity developed within the framework of the Programme in Support of Excellence Groups of the Región de Murcia, Spain, by Fundación Séneca, Regional Agency for Science and Technology (Regional Plan for Science and Technology 2007–2010).
Irene Ortiz was supported by FPU Grant FPU12/02252 from the Ministerio de Educación, Cultura y Deporte, Spain.
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Alías, L.J., Meroño, M.A. & Ortiz, I. On the First Stability Eigenvalue of Constant Mean Curvature Surfaces Into Homogeneous 3-Manifolds. Mediterr. J. Math. 12, 147–158 (2015). https://doi.org/10.1007/s00009-014-0397-y
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DOI: https://doi.org/10.1007/s00009-014-0397-y