A Nash–Kuiper theorem for immersions of surfaces in 3 dimensions
Camillo De Lellis
Universität Zürich, SwitzerlandDominik Inauen
Universität Zürich, SwitzerlandLászló Székelyhidi Jr.
Universität Leipzig, Germany
![A Nash–Kuiper theorem for $C^{1,\frac{1}{5}-\delta}$ immersions of surfaces in 3 dimensions cover](/_next/image?url=https%3A%2F%2Fcontent.ems.press%2Fassets%2Fpublic%2Fimages%2Fserial-issues%2Fcover-rmi-volume-34-issue-3.png&w=3840&q=90)
Abstract
We prove that, given a Riemannian metric on the 2-dimensional disk , any short immersion of into can be uniformly approximated with isometric immersions for any . 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 immersions of surfaces in 3 dimensions. Rev. Mat. Iberoam. 34 (2018), no. 3, pp. 1119–1152
DOI 10.4171/RMI/1019