Abstract
We obtain global extensions of the celebrated Nash–Kuiper theorem for $C^{1,\theta}$ isometric immersions of compact manifolds with optimal Hölder exponent. In particular for the Weyl problem of isometrically embedding a convex compact surface in $3$-space, we show that the Nash–Kuiper non-rigidity prevails upto exponent $\theta \lt 1/5$. This extends previous results on embedding $2$-discs as well as higher dimensional analogues.
Citation
Wentao Cao. László Székelyhidi. "Global Nash–Kuiper theorem for compact manifolds." J. Differential Geom. 122 (1) 35 - 68, September 2022. https://doi.org/10.4310/jdg/1668186787
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