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Discrete and Nondiscrete Isometric Deformations of Surfaces in ℝ3

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Abstract

We prove existence of closed infinitely differentiable surfaces M of \(\mathbb{R}^3 \) each of which can be included in some family F of isometric pairwise noncongruent infinitely differentiable surfaces which is uniformly as close as we want to M. We also prove that F can be more than countable.

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Authors and Affiliations

  1. Departamento de Matematica Pontificia Universidade Catolica Rua Marques de Sao Vicente, 225, 22453-900, Gavea Rio de Janeiro, Brasil

    R. Sa Earp

  2. Departement de Mathematiques Universite Paris VII 2, Place Jussieu, 75251, Paris-Cedex 05, France

    E. Toubiana

Authors
  1. R. Sa Earp
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  2. E. Toubiana
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Sa Earp, R., Toubiana, E. Discrete and Nondiscrete Isometric Deformations of Surfaces in ℝ3 . Siberian Mathematical Journal 43, 714–718 (2002). https://doi.org/10.1023/A:1016384521524

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  • DOI: https://doi.org/10.1023/A:1016384521524

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