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O(m) × O(n)-Invariant Minimal Hypersurfaces in \(\mathbb{R}\)m+n

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Abstract

We classify the nonextendable immersed O(m) × O(n)-invariant minimal hypersurfaces in the Euclidean space \(\mathbb{R}\)m+n, m, n ≥ 3, analyzing also whether they are embedded or stable. We show also the existence of embedded, complete, stable minimal hypersurfaces in \(\mathbb{R}\)m+n, m + n ≥ 8, m, n ≥ 3 not homeomorphic to \(\mathbb{R}\)m+n−1 that are O(m) × O(n)-invariant.

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Authors and Affiliations

  1. Departamento de Matemática, Universidade Federal de Alagoas, 57072-900, Maceió, AL, Brazil

    Hilário Alencar

  2. Departamento de Matemática, Universidade Federal do Ceará, 60455-760, Fortaleza, CE, Brazil

    Abdênago Barros

  3. Facultad de Ciencias, Universidad Nacional Autónoma de México, 04510, México, DF, México

    Oscar Palmas

  4. Departamento de Matemáticas, Universidad Autónoma Metropolitana–Iztapalapa, Av. San Rafael Atlixco 186, Col. Vicentina, 09340, México, DF, México

    J. Guadalupe Reyes

  5. Instituto de Matemática, Universidade Federal do Rio de Janeiro, Av. Brigadeiro Trompowsky, s/n Cidade Universitária, Ilha do Fundão, Caixa Postal 68530, 21945-970, Rio de Janeiro, RJ, Brazil

    Walcy Santos

Authors
  1. Hilário Alencar
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  2. Abdênago Barros
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  3. Oscar Palmas
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  4. J. Guadalupe Reyes
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  5. Walcy Santos
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Correspondence to Hilário Alencar.

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Alencar, H., Barros, A., Palmas, O. et al. O(m) × O(n)-Invariant Minimal Hypersurfaces in \(\mathbb{R}\)m+n. Ann Glob Anal Geom 27, 179–199 (2005). https://doi.org/10.1007/s10455-005-2572-7

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  • DOI: https://doi.org/10.1007/s10455-005-2572-7

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