Publication: A Nash–Kuiper theorem for $C^{1,\frac{1}{5}-\delta}$ immersions of surfaces in 3 dimensions
A Nash–Kuiper theorem for $C^{1,\frac{1}{5}-\delta}$ immersions of surfaces in 3 dimensions
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De Lellis, C., Inauen, D., & Székelyhidi, Jr., László. (2018). A Nash–Kuiper theorem for $C^{1,\frac{1}{5}-\delta}$ immersions of surfaces in 3 dimensions. Revista Matemática Iberoamericana, 34(3), 1119–1152. https://doi.org/10.4171/rmi/1019
Abstract
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Abstract
We prove that, given a $C^2$ Riemannian metric $g$ on the 2-dimensional disk $D_2$, any short $C^1$ immersion of $(D_2,g)$ into $\mathbb{R}^3$ can be uniformly approximated with $C^{1,α}$ isometric immersions for any $α<\frac{1}{5}$. This statement improves previous results by Yu. F. Borisov and of a joint paper of the first and third author with S. Conti.
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- De Lellis, Camillo
- Inauen, Dominik
- Székelyhidi, Jr., László
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De Lellis, C., Inauen, D., & Székelyhidi, Jr., László. (2018). A Nash–Kuiper theorem for $C^{1,\frac{1}{5}-\delta}$ immersions of surfaces in 3 dimensions. Revista Matemática Iberoamericana, 34(3), 1119–1152. https://doi.org/10.4171/rmi/1019
