Abstract

Massot and Theillière showed how one can prove the holonomic approximation lemma using convex integration in the case of first-order jet bundles. In this talk we will discuss a generalization of this idea to higher-order jet bundles using the simplest non-trivial case as a leading example. We will discuss the problems one encounters when trying to generalize this approach and how to solve them. In particular, we will touch upon extending sections of a jet bundle holonomically from a submanifold to an open neighbourhood thereof and a mixed-order version of convex integration.