Zusammenfassung für den Vortrag am 07.10.2020 (11:00 Uhr)

isometric embedding. I first review some conclusions on \(C^{1,\theta}\)

isometric immersions and isometric extension and related problem. Then

I will show our 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. The presented results are joint work with my

mentor Prof. Dr. Szekelyhidi in Leipzig University.