# 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.