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Large spectral gaps for Steklov eigenvalues under volume constraints and under localized conformal deformations

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Abstract

In this paper we construct compact manifolds with fixed boundary geometry which admit Riemannian metrics of unit volume with arbitrarily large Steklov spectral gap. We also study the effect of localized conformal deformations that fix the boundary geometry. For instance, we prove that it is possible to make the spectral gap arbitrarily large using conformal deformations which are localized on domains of small measure, as long as the support of the deformations contains and connects each component of the boundary.

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Authors and Affiliations

  1. Department of Mathematics, University of Michigan, 530 Church Street, Ann Arbor, MI, 48109, USA

    Donato Cianci

  2. Département de Mathématiques et de Statistique, Pavillon Alexandre-Vachon, Université Laval, Quebec, QC, G1V 0A6, Canada

    Alexandre Girouard

Authors
  1. Donato Cianci
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  2. Alexandre Girouard
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Corresponding author

Correspondence to Donato Cianci.

Additional information

Donato Cianci was supported by a CRM-Laval Postdoctoral Fellowship during the year 2016/2017 when this project was started. Alexandre Girouard acknowledges the support of NSERC.

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Cianci, D., Girouard, A. Large spectral gaps for Steklov eigenvalues under volume constraints and under localized conformal deformations. Ann Glob Anal Geom 54, 529–539 (2018). https://doi.org/10.1007/s10455-018-9612-6

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  • DOI: https://doi.org/10.1007/s10455-018-9612-6

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