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Morse index bounds for minimal submanifolds

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Abstract

In this paper, we study the Morse index of closed minimal submanifolds immersed into general Riemannian manifolds. Using the strategy developed by Ambrozio et al. (J Differ Geom 108(3):379–410, 2018) and under a suitable constrain on the submanifold, we obtain that the Morse index of the submanifold is bounded from below by a linear function of its first Betti’s number, as conjectured by Schoen and Marques-Neves. We also present many Riemannian manifolds and a sufficient condition to get the cited linear lower bound.

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Funding

This work was partially supported by Alagoas Research Foundation (FAPEAL), National Council for Scientific and Technological Development (CNPq) [Grant: 308440/2021-8 and 405468/2021-0 to M.B.] and Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)[Finance code - 001 to both authors], Brazil.

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Authors and Affiliations

  1. DME, Universidade do Estado do Rio Grande do Norte, Mossoró, RN, 59610-210, Brazil

    Diego Adauto

  2. CPMAT-IM, Universidade Federal de Alagoas, Maceió, AL, 57072-970, Brazil

    Márcio Batista

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  1. Diego Adauto
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  2. Márcio Batista
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Correspondence to Márcio Batista.

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Adauto, D., Batista, M. Morse index bounds for minimal submanifolds. Collect. Math. 75, 101–127 (2024). https://doi.org/10.1007/s13348-022-00380-7

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  • DOI: https://doi.org/10.1007/s13348-022-00380-7

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