16:00-17:00 Tuesday, 1 April 2025 Auditorium, Rectorate
Abstract
For any given short embedding from an n-dimensional region into $(n-1)$-dimensional Euclidean space, and for any Hölder exponent $\alpha < (n^2 - n + 1)^{-1}$, a $C^{1, \alpha}$ isometric embedding is built within any $C^0$ neighbourhood of the given short embedding through convex integration, which refines the classical Nash-Kuiper theorem and extends the flexibility of $C^{1,\alpha}$ isometric embedding beyond Borisov’s exponent. Notably, when $n = 2$, we attain the Onsager exponent $1/3$ 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.