A Nash–Kuiper theorem for C1,15δC^{1,\frac{1}{5}-\delta} immersions of surfaces in 3 dimensions

  • Camillo De Lellis

    Universität Zürich, Switzerland
  • Dominik Inauen

    Universität Zürich, Switzerland
  • László Székelyhidi Jr.

    Universität Leipzig, Germany
A Nash–Kuiper theorem for $C^{1,\frac{1}{5}-\delta}$ immersions of surfaces in 3 dimensions cover
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Abstract

We prove that, given a C2C^2 Riemannian metric gg on the 2-dimensional disk D2D_2, any short C1C^1 immersion of (D2,g)(D_2,g) into R3\mathbb R^3 can be uniformly approximated with C1,αC^{1,\alpha} isometric immersions for any α<15\alpha < \frac{1}{5}. This statement improves previous results by Yu. F. Borisov and of a joint paper of the first and third author with S. Conti.

Cite this article

Camillo De Lellis, Dominik Inauen, László Székelyhidi Jr., A Nash–Kuiper theorem for C1,15δC^{1,\frac{1}{5}-\delta} immersions of surfaces in 3 dimensions. Rev. Mat. Iberoam. 34 (2018), no. 3, pp. 1119–1152

DOI 10.4171/RMI/1019