| 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 |
PDF:
Order:
2