Resumen de A Nash–Kuiper theorem for C1,15−δ immersions of surfaces in 3 dimensions

Camillo de Lellis, Dominik Inauen, László Székelyhidi

• We prove that, given a C2 Riemannian metric g on the 2-dimensional disk D2, any short C1 immersion of (D2,g) into R3 can be uniformly approximated with C1,α isometric immersions for any α<15. This statement improves previous results by Yu. F. Borisov and of a joint paper of the first and third author with S. Conti.