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Vanishing theorems, higher order mean curvatures and index estimates for self-shrinkers

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Abstract

In this paper we study non-compact self-shrinkers first in general codimension and then in codimension 1. We respectively prove some vanishing theorems giving rise to rigidity of the self-shrinker and then estimates involving the higher order mean curvatures for the oriented case. The paper ends with some results on their index when considered as appropriate \(\bar f\)-minimal hypersurfaces.

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Author information

Authors and Affiliations

  1. Departamento de Matemática, Universidade Federal do Ceará-UFC, 60455-760, Fortaleza, Brazil

    Gregório Pacelli Bessa

  2. Departamento de Matemática, Universidade Federal do Piauí-UFPI, 64049-550, Teresina, Brazil

    Leandro F. Pessoa

  3. Dipartimento di Matematica, Università degli Studi di Milano, Via Saldini 50, Milano, Italy

    Marco Rigoli

Authors
  1. Gregório Pacelli Bessa
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  2. Leandro F. Pessoa
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  3. Marco Rigoli
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Correspondence to Gregório Pacelli Bessa.

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Research partially supported by CNPq-Brazil.

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Bessa, G.P., Pessoa, L.F. & Rigoli, M. Vanishing theorems, higher order mean curvatures and index estimates for self-shrinkers. Isr. J. Math. 226, 703–736 (2018). https://doi.org/10.1007/s11856-018-1703-3

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  • DOI: https://doi.org/10.1007/s11856-018-1703-3

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