Global Nash-Kuiper theorem for compact manifolds

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 $\theta <1/5$. This extends previous results on embedding 2-discs as well as higher dimensional analogues.

31 pages

References in corpus (1)

• $C^{1,\alpha }$ Isometric Embeddings of Polar Caps

Cited by in corpus (2)

• Convexity of weakly regular surfaces of distributional nonnegative intrinsic curvature
• Optimal quantitative stability of the Möbius group of the sphere in all dimensions