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Geometric Properties of Self-Shrinkers in Cylinder Shrinking Ricci Solitons

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Abstract

In this paper, we prove some spectral properties of the drifted Laplacian of self-shrinkers properly immersed in gradient shrinking Ricci solitons. Then we use these results to prove some geometric properties of self-shrinkers. For example, we describe a collection of domains in the ambient space that cannot contain self-shrinkers.

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Acknowledgements

The work was partially supported by CNPq and Faperj of Brazil.

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Authors and Affiliations

  1. Departamento de Matemática, Universidade Federal do Espírito Santo, Vitória, ES, 29075-910, Brazil

    Matheus Vieira

  2. Instituto de Matemática e Estatística, Universidade Federal Fluminense, Niterói, RJ, 24020-140, Brazil

    Detang Zhou

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  1. Matheus Vieira
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  2. Detang Zhou
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Correspondence to Detang Zhou.

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Vieira, M., Zhou, D. Geometric Properties of Self-Shrinkers in Cylinder Shrinking Ricci Solitons. J Geom Anal 28, 170–189 (2018). https://doi.org/10.1007/s12220-017-9815-2

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  • DOI: https://doi.org/10.1007/s12220-017-9815-2

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