A Nash–Kuiper theorem for C1,15−δ immersions of surfaces in 3 dimensions

• Camillo De Lellis ^[1] ; Dominik Inauen ^[1] ; László Székelyhidi Jr. ^[2]
  1. [1] University of Zurich

     University of Zurich

     Zürich, Suiza

     
  2. [2] University of Leipzig

     University of Leipzig

     Kreisfreie Stadt Leipzig, Alemania

     
• Localización: Revista matemática iberoamericana, ISSN 0213-2230, Vol. 34, Nº 3, 2018, págs. 1119-1152
• Idioma: inglés
• DOI: 10.4171/RMI/1019
• Texto completo no disponible (Saber más ...)
• Resumen

  • We prove that, given a C2 Riemannian metric g on the 2-dimensional disk D2, any short C1 immersion of (D2,g) into R3 can be uniformly approximated with C1,α isometric immersions for any α<15. This statement improves previous results by Yu. F. Borisov and of a joint paper of the first and third author with S. Conti.