# Analysis Seminar

#### A Nash-Kuiper Theorem for $$C^{1,1/5}$$ Isometric Immersions of Disks

Speaker: Camillo de Lellis, University of Zurich / Princeton University

Location: Warren Weaver Hall 1302

Date: Thursday, April 21, 2016, 11 a.m.

Synopsis:

In a joint work with Dominik Inauen and László Székelyhidi we prove that, given a $$C^2$$ Riemannian metric $$g$$ on the $$2$$-dimensional disk, any short $$C^1$$ embedding can be uniformly approximated with $$C^{1,\alpha}$$ isometric embeddings for any $$\alpha < \frac{1}{5}$$. The same statement with $$C^1$$ isometric embeddings is a groundbreaking result due to Nash and Kuiper. The previous Hoelder threshold, 1/7, was first announced in the sixties by Borisov. If time allows I will also discuss the connection with a conjecture of Onsager on weak solutions to the Euler equations.