Title A Nash-Kuiper theorem for $C^{1,\frac15-\delta}$ immersions of surfaces in $3$ dimensions Publication Type Journal Article Year of Publication 2018 Authors De Lellis C., Inauen D., L. Székelyhidi Jr. Journal Revista matemática iberoamericana Volume 34 Pagination 1119–1152 Date Published August Publisher Universidad de La Rioja ; Dialnet Type of Article isometric ISSN 0213-2230 Keywords General Mathematics Abstract We prove that and given a \$C\^ 2\$ Riemannian metric \$g\$ on the 2-dimensional disk \$D_2\$ and any short \$C\^ 1\$ immersion of \$(D_2 and g)\$ into \\backslash$mathbb{R}\^ 3\$ can be uniformly approximated with \$C\^ {1 and \ensuremathα}\$ isometric immersions for any \$\ensuremathα\ensuremath<$\backslash$frac{1}{5}\$. This statement improves previous results by Yu. F. Borisov and of a joint paper of the first and third author with Conti, S.. Notes Rev. Mat. Iberoam. 34 (2018) no. 3, 1119-1152 URL https://www.ems-ph.org/journals/show_abstract.php?issn=0213-2230&vol=34&iss=3&rank=9 DOI 10.4171/rmi/1019
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