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arXiv · 1906.08608

Global Nash-Kuiper theorem for compact manifolds

Wentao Cao·László Székelyhidi Jr
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Abstract

We obtain global extensions of the celebrated Nash-Kuiper theorem for $C^{1,\theta}$ isometric immersions of compact manifolds with optimal H\"older 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 $\theta<1/5$. This extends previous results on embedding 2-discs as well as higher dimensional analogues.

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Wentao Cao, László Székelyhidi Jr. 2019-06-20. Global Nash-Kuiper theorem for compact manifolds. https://doi.org/10.4310/jdg%2F1668186787

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