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Bounding the First Dirichlet Eigenvalue of a Tube Around a Complex Submanifold of ℂP n(λ) in Terms of the Degrees of the Polynomials Defining It

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Abstract

We obtain upper bounds for the first Dirichlet eigenvalue of a tube around a complex submanifold P of ℂP n(λ) which depends only on the radius of the tube, the degrees of the polynomials defining P, and the first eigenvalue of the tube around some model centers. The bounds are sharp on these models. Moreover, when the models used are ℂP q(λ) or Q n−1(λ) these bounds also provide gap phenomena and comparison results.

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Acknowledgements

V. Miquel has been partially supported by DGI (Spain) and FEDER Project MTM2010-15444 and the Generalitat Valenciana Project GVPrometeo 2009/099.

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Authors and Affiliations

  1. Departamento de Matemáticas para la Economía y la Empresa, Universidad de Valencia, Avda Tarongers s/n, 46022, Valencia, Spain

    M. Carmen Domingo-Juan

  2. Departamento de Geometría y Topología, Universidad de Valencia, Avda. Andrés Estellés, 1, 46100, Burjassot, Valencia, Spain

    Vicente Miquel

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  1. M. Carmen Domingo-Juan
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  2. Vicente Miquel
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Correspondence to Vicente Miquel.

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Domingo-Juan, M.C., Miquel, V. Bounding the First Dirichlet Eigenvalue of a Tube Around a Complex Submanifold of ℂP n(λ) in Terms of the Degrees of the Polynomials Defining It. J Geom Anal 24, 92–103 (2014). https://doi.org/10.1007/s12220-012-9328-y

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  • DOI: https://doi.org/10.1007/s12220-012-9328-y

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