Abstract
For any given short embedding from an n-dimensional region into -dimensional Euclidean space, and for any Hölder exponent , a isometric embedding is built within any neighbourhood of the given short embedding through convex integration, which refines the classical Nash-Kuiper theorem and extends the flexibility of isometric embedding beyond Borisov’s exponent. Notably, when , we attain the Onsager exponent for isometric embeddings. This convex integration scheme is performed through new construction and leveraging iterative “integration by parts” to effectively transfer large-scale errors to smaller ones. In my talk, I would like to give some ideas for the “integration by parts” procedure. Furthermore, I will highlight the differences between the schemes that were previously used. This is a joint work with Wentao Cao, and Dominik Inauen.
