Geometric Regularity on Regular Manifolds
Résumé
In this talk we discuss an approach to formalize the notion of "regularity", focusing specially on "regularity structures" on $C^k$-manifolds and on geometric objects, such as tensors,partial differential operators, connections on bundles,etc. We present an strategy that could be used to attack existence and multiplicity problems for these regularity structures.The talk is based on joint works arXiv:1908.04442 and arXiv:1910.03113 with Rodney Josué Biezuner, and some working in progress.