On the first stability eigenvalue of constant mean curvature surfaces into homogeneous 3-manifolds

Luis J. Alías; Miguel A. Meroño; Irene Ortiz

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arXiv · 1310.3995

On the first stability eigenvalue of constant mean curvature surfaces into homogeneous 3-manifolds

Luis J. Alías·Miguel A. Meroño·Irene Ortiz

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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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Luis J. Alías, Miguel A. Meroño, Irene Ortiz. 2013-10-15. On the first stability eigenvalue of constant mean curvature surfaces into homogeneous 3-manifolds. https://arxiv.org/abs/1310.3995

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