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Robust index bounds for minimal hypersurfaces of isoparametric submanifolds and symmetric spaces

  • Claudio Gorodski
  • Ricardo A. E. MendesEmail author
  • Marco Radeschi
Article
  • 26 Downloads

Abstract

We find many examples of compact Riemannian manifolds (Mg) whose closed minimal hypersurfaces satisfy a lower bound on their index that is linear in their first Betti number. Moreover, we show that these bounds remain valid when the metric g is replaced with \(g'\) in a neighbourhood of g. Our examples (Mg) consist of certain minimal isoparametric hypersurfaces of spheres, their focal manifolds, the Lie groups \({\text {SU}}(n)\) for \(n\le 17\) and \({\text {Sp}}(n)\) for all n, and all quaternionic Grassmannians.

Mathematics Subject Classification

49Q05 53A10 53C35 53C40 

Notes

Acknowledgements

It is a pleasure to thank Lucas Ambrozio and Alessandro Carlotto for useful discussions, and Alexander Lytchak and the University of Cologne for the hospitality during the visits of the first- and third-named authors.

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Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature 2019

Authors and Affiliations

  • Claudio Gorodski
    • 1
  • Ricardo A. E. Mendes
    • 2
    Email author
  • Marco Radeschi
    • 3
  1. 1.University of São PauloSão PauloBrazil
  2. 2.University of CologneCologneGermany
  3. 3.University of Notre DameNotre DameUSA

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