Resumen de Rigidity and regularity of co-dimension one Sobolev isometric immersions

Zhuomin Liu, Mohammad Reza Pakzad

• We prove the developability and C1,1/2 loc regularity of W2,2 isometric immersions of n-dimensional domains into Rn+1. As a conclusion we show that any such Sobolev isometry can be approximated by smooth isometries in the W2,2 strong norm, provided the domain is C1 and convex. Both results fail to be true if the Sobolev regularity is weaker than W2,2.